Econometric Model To Predict USD INR Exchange Rate Economics Essay
The purpose of this paper is to build a model which successfully predicts the medium/long term USD/INR exchange rate movement. There has been a lot of research and analysis work already in the area of exchange rate prediction as this is an area of interest for Scholars, Business houses, Investors and Governments. While researchers have tried Random walk model and fundamental asset pricing model as well, this paper attempts to predict the exchange rate based on macroeconomic variables using statistical techniques like correlation analysis and stepwise multiple regression analysis.
Analysis was performed on the Quarterly level data for various Indian and American economic indicator variables over the period of 1996 to Q2, 2012.
Data from Qtr 1, 1996 to Qtr 4, 2010 (60 Qtrs) was used for building and training the model and data from Qtr 1, 2011 to Qtr 2, 2012 (6 Qtrs) was used for validating (checking out-of-sample accuracy) the model.
The model which has come out of the research predicts the exchange rate with
70% accuracy within +/-1.5% range of actual Exchange rate
53% accuracy and +/- 1.0% range of actual Exchange rate
44% accuracy and +/-0.75% range of actual Exchange rate
30% accuracy and +/-0.50 range of actual Exchange rate
19% accuracy and +/-0.25 range of actual Exchange rate
As the model is based on macroeconomic variables and no microeconomic variables are taken into consideration, given the time frame, hence, the influence of microeconomic factors is not accounted for in this model, which can pose a margin of error in the prediction.
It is observed that the model is unable to predict the exchange rate for some specific period within accepted residual range; it is likely that some variables which are not considered in the regression equation will need to be accounted for. Hence, there is further scope for this analysis to be extended and study those periods carefully and account for those variables which will add more flavors to the results and reduce the areas where the model is unable to trace the actual price.
Major data sources were – IMF and IFS, American bodies like CSO, BEA, BLS and Reserve Bank of India
Acknowledgement:
This dissertation would not have been possible without the guidance and the help of several individuals who in one way or another contributed and extended their valuable assistance in the preparation and completion of this study.
First and foremost, my utmost gratitude to Dr. Sunil Ashra, Associate Professor, Economics, Management Development Institute whose sincerity and encouragement I will never forget. Mr. Prashant Dabas, Sr. General Manager-R&A, WNS (Holdings) Limited, India has been my inspiration as I hurdle all the obstacles in the completion this research work.
The staff of the MDI Library especially for being accommodating to our requirement to assistant for all the help.
MDI Computer labs for the assistance on how to use the software and downloading of the Journals needed for my Dissertations;
The Administrators of the Faculty of MDI, for their untiring effort in encouraging the Students to pursue professional growth. Likewise the staff of the Dean’s Office for their relaying every communication sent in my behalf.
Last but not the least, my Organization i.e WNS (Holdings) Limited, India and specifically Research & Analytics vertical for providing me such an opportunity.
Table of Contents
Page
Acknowledgement
Abstract (maximum two pages)
Table of Contents
List of Figures
List of Tables
List of Appendices
List of Abbreviations
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1.1
1.2
1.2.1
1.2.2
II XXXXXXXXXX
2.1
2.2
2.1.1
2.1.2
III XXXXXXXXXX
3.1
3.2
List of Figures
(start from separate page)
Figure No. Description Page
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List of Tables
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Table No. Description Page
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List of Appendices
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Table No. Description Page
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Abbreviations
ADF
Augmented Dickey-Fuller test
USD
United States Dollar
INR
Indian National Rupee
GDP
Gross Domestic Product
SAS
Statistical Analysis System
CORR
Procedure Correlation SAS
REG
Procedure Regression in SAS
US_GDP_N
GDP, nominal [bn. USD]
US_GDP_R
GDP, real (2005) [bn.USD]
US_INF_YOY
Inflation [%yoy]
US_FOREX_RES
Foreign exchange reserves [bn.USD]
US_INTR_LT
Interest rate, long term [ppa]
US_INTR_ST
Interest rate, short term [ppa]
US_TB_BOP
Trade balance, BOP [bn. USD]
US_FDI_BOP
Foreign direct investment, net, BOP [bn. USD]
US_S_EXPO_BOP
Exports, services, BOP [bn. USD]
US_M_EXPO_BOP
Exports, merchandise, BOP [bn. USD]
US_INTR_ST_R
Interest rate, short term, real [ppa]
US_INTR_LT_R
Interest rate, long term, real [ppa]
US_GNP
Gross National Product [250000000 USD]
IN_GDP_N
GDP, nominal [bn. INR]
IN_GDP_R
GDP, real (2005) [bn. INR]
IN_INF_YOY
Inflation [%yoy]
IN_FOREX_RES
Foreign exchange reserves [bn. INR]
IN_INTR_LT
Interest rate, long term [ppa]
IN_INTR_ST
Interest rate, short term [ppa] (CF)
IN_TB_BOP
Trade balance, BOP [bn. INR]
IN_FDI_BOP
Foreign direct investment, net, BOP [bn. INR]
IN_S_EXPO_BOP
Exports, services, BOP [bn. INR]
IN_M_EXPO_BOP
Exports, merchandise, BOP [bn. INR]
IN_INTR_ST_R
Interest rate, short term, real [ppa]
IN_EXCH_R_A
Exchange rate INR per USD, aop [INR per US$]
IN_EXCH_R_E
Exchange rate LC per USD, eop [INR per US$]
Introduction:
In today’s truly globalized world, where International trade practices have evolved to a greater extent, keeping a track of the currency exchange rate plays a pivotal role in realization of real profits. Think of a scenario where some export-based company promised to deliver some goods/services at a pre-decided amount in foreign currency at a specified time and somehow within that specified time period the foreign currency becomes cheaper (devaluation of currency happens). So in this scenario the actual realized profits shrink and the exporter may also face losses in some extreme cases (cases where margins are really low). It’s a difficult and unpredictable situation to be in, when one in exposed to the risk of exchange rate fluctuation and economic scenario goes against the company. So, this example clearly shows that Currency exchange rate movement is an important subject of research. Hence, it has been of great interest to various categories of institutions exposed to currency fluctuation risk e.g. Importers, Exporters, International investors etc. With most countries following an open economy today, ability to predict a closer range of Currency exchange rates has become really critical.
We aim to resolve to a certain extent, the kind of unpredictability in the currency exchange rate scenarios, so that institutions, which are exposed to currency fluctuation risks, can make intelligent decisions in such situations. The purpose of this research is to figure out the macro-economic indicators, which may impact the currency exchange rate between two countries and then studying the level of impact these variables could make on the exchange rate. Finally come up with a predictive model, which can predict the future exchange rate, based on macro-economic environment.
If various institutions exposed to currency fluctuation risks can predict the currency exchange rate beforehand they can take more efficient decisions. While on one hand we focus on deriving the predictive model to forecast the currency exchange rates as accurately as possible, on another hand we also believe that short term currency exchange rates depend on micro-economic factors to a greater extent. Change in supply and demand of foreign currency vs. home currency & market sentiments keep on impacting the short-term currency exchange rates. However, the study of micro-economic factors is not under the scope of this research.
Problem Formulation: The purpose of the research is to help out the institutions exposed to the foreign currency exposures to manage the exchange rate risk in an efficient way. The focus will be on the exchange rate between American currency i.e. USD and Indian currency i.e. INR.
We would be studying the quarterly movement of various macro-economic factors from the point of view of American and Indian economy and will try to narrow down on the important drivers to come up with a predictive model.
Literature reviewed: Abundant amount of theoretical and experimental researches is present in the area of Currency exchange rate. Forecasting the exchange rate has been a contentious issue amongst researchers. There have been numerous studies on predicting or forecasting the foreign exchange rate that have been done in various dimensions. This easily shows that with the shrinking trade boundaries and extensive foreign trades, this area of foreign exchange rate prediction keeps on attracting a lot of researchers and scholars across the world. A lot of work has been done by researchers aiming to figure out the hidden trend and in estimating the exchange rate behavior. With the increase in international trade practices various economists across the globe are continuously trying to figure out the determinants of the fluctuations in currency exchange rates.
Study on Model based on fundamentals
In 1995, Nelson C. Mark found out that the models were helpful in predicting exchange rates at long horizons. After studying the data for five large economies, Mark found that the regressions of multiple period changes in the log exchange rate on the deviation of the log exchange rate display robust evidence of long horizon changes in log nominal exchange rates. According to the paper, the noise generated by short horizon changes is averaged out over time, enabling the exchange rate movements to be determined by the fundamentals. In his research, he shows that the coefficient estimates display a pattern with nominal rigidities, though gradually, but it causes the exchange rate to adjust to nominal or real shocks. For three of the four exchange rates studied by him, the out of sample forecasts outperform the drift less random walk at the longer horizons. He investigated the extent to which deviations of the exchange rate from a fundamental value are useful in predicting exchange rates in the long run. The empirical work was restricted to an analysis of a regression on one variable, in order to conveniently characterize the predictive relation.
Though his empirical work had achieved great success in finding the empirical relativity between exchange rate and fundamentals, but the research had certain limitations as relative time series was short making the asymptotic reference as unreliable.
Subsequent work had casted doubts on forecasting the exchange rate at long horizons. There are certain schools of thoughts that believe in the forecasting power of non linear models. The models come into play in predicting the exchange rate when they are far out of line with the fundamentals.
Present Value models of exchange rate
It was believed that many exchange rate models can be written so that they can be explained as a weighted sum of current fundamentals like money supply, prices, output levels and the expected future value of the exchange rate, putting little weight on current fundamentals as compared to the expectations. Engel and West, in 2004, questioned this standard criterion, and found that, for this class of models, if the fundamentals are integrated of order 1 (that is, their first difference is stationary), and the discount factor is close to one, then the exchange rate will approximately follow a random walk. According to their research, exchange rate is determined by the fundamentals, but floating exchange rate between countries with different inflation rates are well approximated as random walks. They found evidence, for the link between exchange rate and fundamentals, being consistent with the assets pricing models of the exchange rate. They first proved how random walk in asset pricing may result from a discount factor near one in a present value model. They applied this theorem to various exchange rate models successfully and displayed evidence that the changes in the exchange rate help future fundamentals
M. B. Devereux and C. Engel, in 2006, studied on “Expectations and Exchange Rate Policy”. The paper talks about the implications of the fact that exchange rates respond primarily to news about future fundamentals. According to the new Keynesian economics, the aim should be at eliminating the distortions that occur due to sticky nominal prices. In the ideal state, monetary policy should try to reproduce the outcome that would be achieved if nominal prices were flexible. But the problem comes, when in an open economy, the nominal exchange rate of any country pair responds to news about the future, taking into account that there are nominal goods prices that are set in the currency of each country. Then with the change in the nominal exchange rate the relative prices (-the prices of goods set in one currency relative to those set in another currency) are bound to change. The problem is that these relative prices are changing at times when there is news about the future fundamentals, the drivers of the nominal exchange rate. And if good prices were flexible, then relative goods prices would not be influenced by news about the future that is driving the nominal exchange rate. The research puts an argument on the fact that, since most of the variation in exchange rates comes from the news about these future fundamentals; most exchange rate variation generates inefficient relative price movements. They argue that there is a case for monetary policy to target unexpected changes in nominal exchange rates in addition to targeting inflation.
There have been numerous other studies and research work that have been done, but there seems to be no unanimous agreement about predicting/ forecasting the exchange rate.
.
In a paper “Forecasting exchange rates in transition economies: A comparison of multivariate time series models” Cuaresma and Hlouskova compares the accuracy in forecasting through various multivariate models such as unrestricted VAR, BVAR, VEC, Bayesian VEC and deterministically restricted VAR, when applied to forecasting the exchange rate of different Central and Eastern European currencies against the Euro and the US dollar. Several factors have been studied, that determines the exchange rate in such economies, termed by Cuaresma and Hlouskova as transition economies. The results extend and confirm the conclusions in Meese and Rogoff (1983) and presents further evidence on the difficulties found by more sophisticated time series models (in this case VAR, VEC, BVAR, BVEC and restricted VAR models in different specifications) in outperforming the naive forecasts of the random walk for exchange rates. (Res.)
In another paper from FLORIDA INTERNATIONAL UNIVERSITY Miami, Florida named “ESSAYS ON EXCHANGE RATE ECONOMICS” Yan Shu (2008) studied the issues related to comprehending the exchange rate behavior better. It is evident from the vast research available on this topic that modeling and forecasting exchange rates depends on lot variables, whose behavior pattern and impact of exchange rate is difficult to determine. Decades ago, Meese and Rogoff (1983) empirically analyzed several important macro-structural models based on monetary and asset theories of exchange rate determination. They found that none of these models could outperform the naïve random walk model in terms of out-of-sample forecast accuracy at the short horizons. Several researchers post this confirmed the findings for a number of exchange rates.
A lot of literature is available on time series techniques on exchange rate movements. Many researchers have pursued nonlinear modeling of exchange rates, but with little success. (Res)
The Research Problem:
After studying the limitations of modeling the exchange rate behavior by lots of researchers and scholars in the past and several efforts which are still going on, this research paper attempts to study and derive the following:-
Movement in the USD/INR exchange rate
The factors which affect the movement in USD/INR exchange rate
Econometric model to predict USD/INR exchange rate
Challenges & Issues faced during this model development and scope for further refinement and fine-tuning
Assumptions made:
Economic conditions of US and India are only responsible in driving the USD/INR exchange rate and no other country’s economy drives this combination of exchange rate in longer run
Indian Rupee and US Dollar are fully floating currency and both the countries are not making any explicit effort to drive the exchange rates
The Research Design:
Methodology adopted for study
Various economic indicators were studied to gauge their impact on the USD/INR exchange rate in both American and Indian scenario and following variables were finally narrowed down to study further
USA
GDP, nominal [bn. USD]
GDP, real (2005) [bn.USD]
Inflation [%yoy]
Foreign exchange reserves [bn.USD]
Interest rate, long term [ppa]
Interest rate, short term [ppa]
Trade balance, BOP [bn. USD]
Foreign direct investment, net, BOP [bn. USD]
Exports, services, BOP [bn. USD]
Exports, merchandise, BOP [bn. USD]
Interest rate, short term, real [ppa]
Interest rate, long term, real [ppa]
Gross National Product [250000000 USD]
Unemployment rate, U.S.A
Brent Crude Oil Spot Price
Spot gold price in USD
INDIA
GDP, nominal [bn. LC]
GDP, real (2005) [bn. LC]
Inflation [%yoy]
Foreign exchange reserves [bn. LC]
Interest rate, long term [ppa]
Interest rate, short term [ppa]
Trade balance, BOP [bn. LC]
Foreign direct investment, net, BOP [bn. LC]
Exports, services, BOP [bn. LC]
Exports, merchandise, BOP [bn. LC]
Interest rate, short term, real [ppa]
Exchange rate
Exchange rate LC per USD, Average, Average of Period
Exchange rate LC per USD, End of Period
Various types of statistical techniques have been used to study the relationship between these variables and then econometric modeling has been used to derive a causation relationship among various economic factors (independent variables) and USD/INR exchange rate (dependent variable).
Sample data and data source:
Data for all the required variables doesn’t get changed/published at a very high frequency e.g. daily or monthly so data for all the variables was collected at the quarterly level only
Data was collected from Quarter 1, 1990 till Quarter 2, 2012.
Below is the snapshot of the data tables
Sample data India (Table 1)
India
1997Q1
1997Q2
1997Q3
1997Q4
1998Q1
1998Q2
1998Q3
1998Q4
GDP, nominal [bn. INR]
3,669.09
3,688.36
3,845.60
4,038.85
4,148.94
4,308.27
4,479.20
4,551.04
GDP, real (2005) [bn. INR]
5,446.51
5,435.55
5,643.35
5,744.39
5,788.79
5,841.12
5,957.34
6,079.34
Inflation [%yoy]
10.60
7.74
5.18
5.45
9.02
10.35
15.51
17.79
Foreign exchange reserves [bn. INR]
802.48
909.82
925.75
913.01
1,019.73
975.46
1,115.33
1,143.70
Interest rate, long term [ppa]
13.51
12.77
11.70
11.00
12.70
12.05
12.22
12.25
Interest rate, short term [ppa] (CF)
14.75
14.25
13.50
13.00
14.00
13.32
12.83
12.83
Trade balance, BOP [bn. INR]
-119.22
-147.84
-96.98
-172.81
-160.29
-194.66
-143.63
-145.48
Foreign direct investment, net, BOP [bn. INR]
28.13
40.85
27.57
29.07
33.16
37.92
20.34
14.19
Exports, services, BOP [bn. INR]
74.12
79.47
76.99
100.71
93.83
123.86
137.97
128.08
Exports, merchandise, BOP [bn. INR]
334.92
310.69
323.87
326.41
365.85
316.57
372.63
349.42
Interest rate, short term, real [ppa]
3.75
6.05
7.91
7.17
4.56
2.71
-2.32
-4.21
Exchange rate INR per USD, aop [INR per US$]
35.88
35.81
36.03
37.54
39.26
40.76
42.60
42.43
Exchange rate LC per USD, eop [INR per US$]
35.91
35.82
36.18
39.28
39.50
42.47
42.49
42.48
Sample Data U.S.A (Table 2)
United States
1997Q1
1997Q2
1997Q3
1997Q4
1998Q1
1998Q2
1998Q3
1998Q4
GDP, nominal [bn. USD]
2,034.25
2,069.20
2,102.48
2,126.43
2,150.15
2,174.65
2,211.80
2,256.88
GDP, real (2005) [bn.USD]
2,414.50
2,450.30
2,481.05
2,500.08
2,523.70
2,546.40
2,580.00
2,624.65
Inflation [%yoy]
2.94
2.30
2.23
1.89
1.48
1.58
1.60
1.53
Foreign exchange reserves [bn.USD]
32.45
32.93
32.06
30.81
30.22
31.17
32.88
36.00
Interest rate, long term [ppa]
6.56
6.70
6.24
5.91
5.59
5.60
5.20
4.67
Interest rate, short term [ppa]
5.06
5.05
5.05
5.09
5.05
4.98
4.82
4.25
Trade balance, BOP [bn. USD]
-51.54
-47.05
-47.82
-52.02
-56.61
-62.94
-63.80
-64.88
Foreign direct investment, net, BOP [bn. USD]
-4.00
-3.61
-4.28
12.66
-25.19
-25.84
2.15
85.27
Exports, services, BOP [bn. USD]
62.52
64.29
64.86
64.43
64.69
66.17
64.79
67.11
Exports, merchandise, BOP [bn. USD]
162.67
170.25
173.16
172.29
171.06
165.56
164.05
169.74
Interest rate, short term, real [ppa]
2.05
2.68
2.76
3.14
3.52
3.34
3.18
2.69
Interest rate, long term, real [ppa]
3.62
4.35
4.04
4.03
4.13
3.99
3.61
3.13
Gross National Product [250000000 USD]
8,160.10
8,307.70
8,433.10
8,522.30
8,626.00
8,721.40
8,856.80
9,039.00
Brent Crude Oil Price Dollars Per Barrel
18.53
18.22
19.96
15.86
13.87
11.84
14.71
10.54
Gold Price USD
351.30
343.00
323.60
307.70
294.20
299.70
288.90
294.00
Quarter End Unemployment rate
5.20
5.00
4.90
4.70
4.70
4.50
4.60
4.40
Data sources: Various Indian, American and International data and statistics sources were referred for obtaining the required data for all the above mentioned variables. Below is the detailed list of the sources from where the data was downloaded online:
IHS Global Insight
International Monetary Fund (IMF)
International Financial Statistics (IFS)
Reserve Bank of Indiawww.rbi.org.in
Central Statistical Organization
Bureau of Economic Analysis
World Gold Council (http://www.gold.org/investment/statistics/)
Bureau of Labor Statistics (http://www.bls.gov/)
U.S. Energy Information Administration (http://www.eia.gov/)
Data analysis
Selection of time period to study currency exchange rate movement.
Quarterly level data from Quarter 1, 1990 till Quarter 2, 2012 was collated for all the above mentioned economic indicators. But all the data usage was not possible in model formation. Here the aim is to derive the model for predicting currency exchange rate and it can’t be modeled over the period when the USD/INR exchange rate was fixed or pegged. Modeling can only be performed over the period when USD/INR exchange rate actually started floating.
USD/INR exchange rate before 1991 – In 1991, India still had a fixed exchange rate system, where the rupee was pegged to the value of a basket of currencies of major trading partners. India started having balance of payments problems since 1985, and by the end of 1990, it found itself in serious economic trouble. The government was close to default and its foreign exchange reserves had dried up to the point that India could barely finance three weeks’ worth of imports. (Res.)
USD/INR exchange rate after 1991 – Before 1990s was period of severe economic crisis for India and in 1991, the Indian government decided to go for several reforms which led to the liberalization of Indian economy and hence opening the door for foreign investments.
The initiation of economic reforms saw, among other measures, a two-step downward exchange rate adjustment by 9 per cent and 11 per cent between July 1 and 3, 1991 to counter the massive draw down in the foreign exchange reserves, to install confidence in the investors and to improve domestic competitiveness. The Liberalized Exchange Rate Management System (LERMS) was put in place in March 1992 involving the dual exchange rate system in the interim period. The dual exchange rate system was replaced by a unified exchange rate system in March 1993. The experience with a market determined exchange rate system in India since 1993 is generally described as ‘satisfactory’ as orderliness prevailed in the Indian market during most of the period. Episodes of volatility were effectively managed through timely monetary and administrative measures. (Res.). After 1993, Rupee actually started floating.
This forms the basis of the time-window over which we would focus our analysis of USD/INR exchange rate and we extracted data points of USD/INR exchange rate and driving factors over this time-window.
Selection of driver variables – US and India economic indicators
Among various macro-economic indicators present we carefully selected few of them and we would explain one by one the reason behind selecting these variables
1. Economic growth (GDP, GNP): Growth in the country’s economy that is reflected through its GDP/GNP numbers indicates the strength of the economy. Increase in GDP could mean increased demand for the domestic currency or increase in supply of foreign currency in the economy as investments
2. Inflation: Rising inflation indicates lesser purchasing power of the domestic currency compared to other currencies, hence lower exchange rate. It has been observed that country’s with high inflation typically see depreciation of their currency vis a vis developed economies with lower inflation rates
3. Interest Rates: Interest rates play an important role in determining the exchange rates. Higher interest rates would mean higher foreign investments which would drive the currency to rise
4. Current Account Balance: A deficit in the current account balance means that the country has a negative balance of trade and has to pay more in terms of foreign currency. Hence, the domestic country would borrow more in foreign currency to pay off its debts. The excess demand for foreign currency lowers the exchange rate
5. Exports: higher exports would mean greater demand real appreciation of the domestic currency
6. Foreign Direct Investments: In today’s global economy, FDIs are an important factor affecting exchange rates. If the domestic country attracts more foreign currency through FDIs, it would mean appreciation of the domestic currency and vis-à-vis.
Trend Analysis Factor vs. Exchange rate movement
Selected Macro-economic factors’ (Indian and American) movement over the period w.r.t. the movement in USD/INR exchange rate
Its clearly seen that between 2008 and 2009 when US GDP (Nominal) was declining and Indian GDP (Nominal) was increasing sharply a dip in Exchnage rate was seen when value of 1USD came down from Rs 50 to Rs 45.
US inflation figures clearly show a negative correlation between the Inlfation percentages and USD/INR rates.
Forex reserve figures are not showning as such any impact on the past Exhange rate figures as such for both Indian and American markets but it would be more clear when we’ll model the data to check the causation effect.
US long term interest rates are clearly showing some impact on the value of USD vs. Indian Rupee
Short term Interest rate doesn’t seem to play much role in defing the long term term currrency exchnage rate movements.
Trade Balance figures for both US and India clearly showing some impact on the exchnage rates, where a relative increase in Trade Balance figure for US shows strong USD vs Rupee and similarly a relatuve decrease in Trade Balance figure for India shows stornd USD vs Rupee.
Services export figures for India has seen a great growth in last decade but still need to be at that level so that this factor can clearly make an impact on USD/INR exchnage rate
U.S. quarterly published unemployement figures might be impacting the value of USD alone but we would need to check its impact on USD/INR exchnage rate.
Brent cude oil price seems to have a negative relation with the exchnage rate figures as a price increase in crude shows a weaker USD vs. Rupee and a price decrease in crude oil shows a stronger USD ve. Rupee
International gold prices and demand for gold as an investment option also seems to be impactinf the exchange rates.
Testing data for stationarity
In financial modeling while dealing with the time-series data it’s a quite common problem where a naïve analyst misinterprets a high R2 (Co-efficient of determination) in the regression model which shows a good causation relationship between independent and dependent variables that too with significant t-statistics as a good model. But these models on practical ground do not show good outputs while applied and do not hold any economic meaning.
This problem is called “Spurious Regression” termed by Granger and Newbold (1974) (Res.)
These kind of results generally have regression equations with high degree of fit, as measured by R2 , but they have an extremely low-value for Durbin-Watson statistics.
This leads to various kinds of problems e.g. Inefficient Coefficient estimation thus leading to inefficient regression equation, Wrong forecasting/prediction based on inefficient regression equations, Misleading significance tests while selecting/rejecting variables and associated coefficients.
Reason behind all these problems is one and i.e. Non-stationary time series data and if the series is non-stationary, it becomes difficult to represent that series over past and future time-periods by a simple linear arithmetical equation.
Thus each and every time-series of data before entering into any kind of modeling exercise must be tested for non-stationarity or in other words must be checked whether that particular series has unit root.
We have tested each and every variable on the stationarity parameter using a tool called EViews( Res).
In EViews tool there is a test for testing the nonstationarity (has unit root) of the series which is called Augmented Dickey-Fuller(ADF) Test
Using Augmented Dickey-Fuller test one can easily test for unit root in “Level”, “1st difference” and “1st Log-difference” at different lagged differences and at the same time Intercept and Trend can also be included in the test. A screenshot below can easily show the kind of options present in the Unit root test while running with EViews
Below are the few snapshots of the actual test performed on few of the variables in our data
ADF Unit root test for “US GDP, real” series data
Null Hypothesis: (US_GDP_R) has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=10)
t-Statistic
Augmented Dickey-Fuller test statistic
-2.128171
Test critical values:
1% level
-3.544063
5% level
-2.910860
10% level
-2.593090
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D((US_GDP_R))
Method: Least Squares
Date: 09/27/12 Time: 20:56
Sample: 1996Q1 2010Q4
Included observations: 60
Variable
Coefficient
Std. Error
t-Statistic
US_GDP_R(-1)
-0.016545
0.007774
-2.128171
D((US_GDP_R(-1)))
0.422163
0.116338
3.628760
C
57.99790
23.50414
2.467561
R-squared
0.305301
Mean dependent var
Adjusted R-squared
0.280925
S.D. dependent var
S.E. of regression
17.79354
Akaike info criterion
Sum squared resid
18046.77
Schwarz criterion
Log likelihood
-256.3276
F-statistic
Durbin-Watson stat
2.125536
Prob(F-statistic)
Screenshot above clearly shows the “Null Hypothesis: US_GDP_R has a unit root”
Result of Test:
A higher value of “Augmented Dickey-Fuller test statistic i.e. -2.128171” than “Test critical values” cannot reject the Null hypothesis and thus this series has a unit root at level.
Although it has high value for “Durbin-Watson stat i.e. 2.125536” but it does not pass the above result to reject the null hypothesis
Now, once the series is nonstationary at level we can test the series again for nonstationairty at 1st log-difference level
Null Hypothesis: DLOG(US_GDP_R) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=10)
t-Statistic
Augmented Dickey-Fuller test statistic
-4.367257
Test critical values:
1% level
-3.544063
5% level
-2.910860
10% level
-2.593090
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DLOG(US_GDP_R))
Method: Least Squares
Date: 09/27/12 Time: 18:51
Sample: 1996Q1 2010Q4
Included observations: 60
Variable
Coefficient
Std. Error
t-Statistic
DLOG(US_GDP_R(-1))
-0.494802
0.113298
-4.367257
C
0.002978
0.001057
2.817445
R-squared
0.247466
Mean dependent var
Adjusted R-squared
0.234491
S.D. dependent var
S.E. of regression
0.006230
Akaike info criterion
Sum squared resid
0.002251
Schwarz criterion
Log likelihood
220.5862
F-statistic
Durbin-Watson stat
2.237665
Prob(F-statistic)
Again the test has the same “Null Hypothesis: DLOG(US_GDP_R) has a unit root”. But this time test is being performed at 1 Log-difference level
Result of Test:
A lower value of “Augmented Dickey-Fuller test statistic i.e. -4.367257” than “Test critical values” is seen so we can reject the Null hypothesis and thus this series has not a unit root at 1st difference.
And a high value for “Durbin-Watson stat i.e. 2.237665” further strengthens the result to reject the null hypothesis
Conclusion of the ADF unit root test on “US GDP, real” series data
If this series data is used as it is (at level) into regression modeling, due to nonstationarity of the series this may lead to spurious regression and hence associated problems discussed above
But if this series data is used at 1st difference into regression modeling, due to stationarity at 1st difference level it will prevent any such problem of spurious regression.
Below are some more snapshots of ADF unit root test on one more variable
Null Hypothesis: US_FDI_BOP has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=10)
t-Statistic
Augmented Dickey-Fuller test statistic
-3.824404
Test critical values:
1% level
-3.544063
5% level
-2.910860
10% level
-2.593090
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(US_FDI_BOP)
Method: Least Squares
Date: 09/27/12 Time: 18:57
Sample: 1996Q1 2010Q4
Included observations: 60
Variable
Coefficient
Std. Error
t-Statistic
US_FDI_BOP(-1)
-0.654682
0.171185
-3.824404
D(US_FDI_BOP(-1))
-0.277228
0.127168
-2.180012
C
-4.721387
5.188665
-0.909943
R-squared
0.495422
Mean dependent var
Adjusted R-squared
0.477717
S.D. dependent var
S.E. of regression
38.91797
Akaike info criterion
Sum squared resid
86332.70
Schwarz criterion
Log likelihood
-303.2849
F-statistic
Durbin-Watson stat
2.056532
Prob(F-statistic)
A lower value of “Augmented Dickey-Fuller test statistic i.e. -3.824404” than “Test critical values” is at level only shows that we can reject the Null hypothesis and thus this series has not a unit root at level only and can be used at it is in our further analysis.
Here are the summarized results of the Unit root test using ADF
Variable
Variable desc
Unit root test (Augmented Dickey-Fuller test)
US_GDP_N
GDP, nominal [bn. USD]
Has unit root at level
has NOT Unit Root at Log-difference level
US_GDP_R
GDP, real (2005) [bn.USD]
Has unit root at level
has NOT Unit Root at Log-difference level
US_INF_YOY
Inflation [%yoy]
Has unit root at level
has NOT Unit Root at 1st difference level
US_FOREX_RES
Foreign exchange reserves [bn.USD]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
US_INTR_LT
Interest rate, long term [ppa]
Has unit root at level
has NOT Unit Root at 1st difference level
US_INTR_ST
Interest rate, short term [ppa]
Has unit root at level
has NOT Unit Root at 1st difference level
US_TB_BOP
Trade balance, BOP [bn. USD]
Has unit root at level
has NOT Unit Root at 1st difference level
US_FDI_BOP
Foreign direct investment, net, BOP [bn. USD]
has NOT Unit Root level
US_S_EXPO_BOP
Exports, services, BOP [bn. USD]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
US_M_EXPO_BOP
Exports, merchandise, BOP [bn. USD]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
US_INTR_ST_R
Interest rate, short term, real [ppa]
Has unit root at level
has NOT Unit Root at 1st difference level
US_INTR_LT_R
Interest rate, long term, real [ppa]
Has unit root at level
has NOT Unit Root at 1st difference level
US_GNP
Gross National Product [250000000 USD]
Has unit root at level
has NOT Unit Root at 1st difference level
IN_GDP_N
GDP, nominal [bn. INR]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
IN_GDP_R
GDP, real (2005) [bn. INR]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
IN_INF_YOY
Inflation [%yoy]
Has unit root at level
has NOT Unit Root at 1st difference level
IN_FOREX_RES
Foreign exchange reserves [bn. INR]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
IN_INTR_LT
Interest rate, long term [ppa]
Has unit root at level
has NOT Unit Root at 1st difference level
IN_INTR_ST
Interest rate, short term [ppa] (CF)
Has unit root at level
has NOT Unit Root at 1st difference level
IN_TB_BOP
Trade balance, BOP [bn. INR]
Has unit root at level
has NOT Unit Root at 1st difference level
IN_FDI_BOP
Foreign direct investment, net, BOP [bn. INR]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
IN_S_EXPO_BOP
Exports, services, BOP [bn. INR]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
IN_M_EXPO_BOP
Exports, merchandise, BOP [bn. INR]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
IN_INTR_ST_R
Interest rate, short term, real [ppa]
Has unit root at level
has NOT Unit Root at 1st difference level
IN_EXCH_R_A
Exchange rate INR per USD, aop [INR per US$]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
IN_EXCH_R_E
Exchange rate LC per USD, eop [INR per US$]
Has unit root at level
has NOT Unit Root at 1st Log-difference level
Qtr_End_Unemp
Quarter End Unemployment rate
Has unit root at level
has NOT Unit Root at 1st difference level
BrentCrude_USD_Barrel
Brent Crude Oil in Dollars per Barrel
Has unit root at level
has NOT Unit Root at 1st Log-difference level
Gold_Price_USD
Gold Price in USD
Has unit root at level
has NOT Unit Root at 1st Log-difference level
After testing all the time-series variables for nonstationarity we have converted them at required level of difference (either 1st difference or 1st Log-difference) as mentioned in the table above.
Now, we can easily use these stationary time series variables for further analysis
Building regression model
To build the predictive model we’ll use LS- Least Squares (NLS and ARMA) regression analysis using the package called EViews
Data Sampling
We have data available for the period of last 66 Quarters starting Quarter 1, 1996 till Quarter 2, 2012 for all the variables we have selected above for our analysis
To facilitate the cross-validation of our model we can’t build the model on the data available for all the 66 quarters
Cross-validation is a technique for assessing how the results of a statistical analysis will generalize to an independent data set in future. It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice (Res.)
In-sample (Training data set) – We’ll use the first 60 quarters (Quarter 1, 1996 till Quarter 4, 2010) of data series as Training data set on which the model will be build
Out-of sample (Validation data set) – We’ll use the last 6 quarters (Quarter 1, 2011 till Quarter 2, 2012) of data series as Validation data set on which we’ll test the model
Regression Analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. (Res.)
We have tested various models on EViews and we’ll be presenting the best model here:
Model 1:
Estimation Command:
=====================
LS DLOG(IN_EXCH_R_A) C DLOG(IN_GDP_R(-2)) DLOG(IN_GDP_R(-1)) DLOG(US_GDP_R) DLOG(US_GDP_R(-2)) DLOG(IN_FOREX_RES(-1)) DLOG(GOLD_PRICE_USD(-4)) D(IN_INF_YOY) D(US_INF_YOY) DLOG(US_S_EXPO_BOP(-2))
Estimation Equation:
=====================
DLOG(IN_EXCH_R_A) = C(1) + C(2)*DLOG(IN_GDP_R(-2)) + C(3)*DLOG(IN_GDP_R(-1)) + C(4)*DLOG(US_GDP_R) + C(5)*DLOG(US_GDP_R(-2)) + C(6)*DLOG(IN_FOREX_RES(-1)) + C(7)*DLOG(GOLD_PRICE_USD(-4)) + C(8)*D(IN_INF_YOY) + C(9)*D(US_INF_YOY) + C(10)*DLOG(US_S_EXPO_BOP(-2))
Regression output
Dependent Variable: DLOG(IN_EXCH_R_A)
Method: Least Squares
Date: 09/27/12 Time: 18:00
Sample (adjusted): 1996Q4 2010Q4
Included observations: 57 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
C
0.031001
0.006486
4.779859
DLOG(IN_GDP_R(-2))
-0.499163
0.170047
-2.935435
DLOG(IN_GDP_R(-1))
-0.463870
0.178224
-2.602730
DLOG(US_GDP_R)
-2.107391
0.433632
-4.859865
DLOG(US_GDP_R(-2))
2.185960
0.422857
5.169507
DLOG(IN_FOREX_RES(-1))
-0.118207
0.047920
-2.466778
DLOG(GOLD_PRICE_USD(-4))
-0.137674
0.045663
-3.014999
D(IN_INF_YOY)
0.003546
0.001188
2.985050
D(US_INF_YOY)
-0.010185
0.003063
-3.325615
DLOG(US_S_EXPO_BOP(-2))
-0.222063
0.096062
-2.311654
R-squared
0.662614
Mean dependent var
Adjusted R-squared
0.598009
S.D. dependent var
S.E. of regression
0.017453
Akaike info criterion
Sum squared resid
0.014317
Schwarz criterion
Log likelihood
155.3675
F-statistic
Durbin-Watson stat
1.729332
Prob(F-statistic)
**In statistics, the coefficient of determination R2 is used in the context of statistical models whose main purpose is the prediction of future outcomes on the basis of other related information. It is the proportion of variability in a data set that is accounted for by the statistical model.[1] It provides a measure of how well future outcomes are likely to be predicted by the model. (Res.)
Interpretation of regression results
‘
Dependent Variable: DLOG(IN_EXCH_R_A) Log difference of Quarterly average of Exchange rate is to modeled to be predicted
Below is the list of predictors which are predicting the Exchange rate at +97% confidence levels:
DLOG(IN_GDP_R(-2)) – Log difference of Indian GDP, real at lag of 2 quarters
DLOG(IN_GDP_R(-1)) – Log difference of Indian GDP, real at lag of 1 quarter
DLOG(US_GDP_R) – Log difference of US GDP, real
DLOG(US_GDP_R(-2)) – Log difference of GDP, real at lag of 2 quarters
DLOG(IN_FOREX_RES(-1)) – Log difference of Indian Forex Reserves at lag of 1quarter
DLOG(GOLD_PRICE_USD(-4)) – Log difference of US Gold prices at lag of 4 quarters (approx. 1year)
D(IN_INF_YOY) – 1st difference of India’s Inflation rate, YoY
D(US_INF_YOY) – 1st difference of US Inflation rate, YoY
DLOG(US_S_EXPO_BOP(-2)), Log difference of Exports, services, BOP at lag of 2 quarters
R-squared 0.662614 shows R2 (Coefficient of determination) of 66% which depicts that above model 66% variance in the Dependent variable is explained by predictor variables, which is acceptable in econometrics when all the variables are stationary.
Also, all the predictor variables are highly significant in the model as Prob. value for all the variables are less than 0.252 which means all of the variables are significant at +97% confidence level which is again an acceptable significant level.
Average Exchange rate (Actual vs. Predicted) Residual Graph
Below is the chart depicting model Predicted movement in the Exchange rate vs. Actual exchange rate.
This chart also depicts the residual error within the range of 2%. For most of the periods our prediction of currency exchange rate is within 2% range of residual.
Final Model Equation for Exchange rate prediction
Below is the final model equation which can be used for predicting log difference value in Quarterly average Exchange rate:-
=================================================================================
DLOG(IN_EXCH_R_A) = 0.03100115483 –
0.4991631092*DLOG(IN_GDP_R(-2)) –
0.4638700812*DLOG(IN_GDP_R(-1)) –
2.107391256*DLOG(US_GDP_R) +
2.185959966*DLOG(US_GDP_R(-2)) –
0.1182073631*DLOG(IN_FOREX_RES(-1)) – 0.1376737418*DLOG(GOLD_PRICE_USD(-4)) +
0.003546025185*D(IN_INF_YOY) –
0.01018485955*D(US_INF_YOY) –
0.2220630033*DLOG(US_S_EXPO_BOP(-2))
=================================================================================
Measuring the accuracy of the Regression Model
As mentioned earlier, below is the chart and metrics depicting the trained model’s validation on out-of sample data points
Cross validation sample (Out-of-sample) forecast chart
While predicting the log difference of exchange rate on the out-of-smaple periods i.e. from Quarter 1, 2011 to Quarter 2, 2012, Root Mean Squared Error comes out to be 0.047
While predicting the exchange rate on the out-of-smaple periods i.e. from Quarter 1, 2011 to Quarter 2, 2012, Root Mean Squared Error comes out to be 5.03
Average USD/INR Exchange rate movement figures
It has been seen that average quarterly movement in USD/INR Exchange rate since Q1, 1996 is within 2.0% range, so anything which can narrow down this range during prediction will add to the prediction accuracy.
Predictability accuracy at different range of residuals
Exchange rate Prediction Accuracy within 1.5% range
Exchange rate Prediction Accuracy within 1.0% range
Exchange rate Prediction Accuracy within 0.75% range
Exchange rate Prediction Accuracy within 0.50% range
Exchange rate Prediction Accuracy within 0.25% range
70%
53%
44%
30%
19%
Conclusions and Recommendations:
This piece of analysis work has provided a step towards the “macro-economic factors driven” exchange rate prediction model. In compared to the most of the work done where the prediction is based on the past hidden trend within the exchange rate time-series only, this model further try to train itself in a more fine-tuned way to get more closer predictions more number of times.
Indian Rupee is floating now for almost 20+ years now and has seen highs and lows. Indian Rupee has seen many actions in the form policies from Indian Government and other economic institutions and responded as well. It has seen action from various Indian Importers, Exporters, and International Investors as well at different point of time. Apart from a short term demand and supply trends, in medium and long-run Indian Rupee vs. USD exchange rate movement has clearly followed the outcomes of all these actions whether happening in India or US
Out of many possible macro level factors we have found out few factors which clearly show their impact on the exchange rate and thus make exchange rate predictions much more efficient than a regular trending exercise or a mere guess. In the order from timely to late impact below are the key driver factors impacting the exchange rates
Predictors Impacting the Exchange rate in the same Quarter
DLOG(US_GDP_R) – Log difference of US GDP, real
D(IN_INF_YOY) – 1st difference of India’s Inflation rate, YoY
D(US_INF_YOY) – 1st difference of US Inflation rate, YoY
Predictors Impacting the Exchange rate in the next Quarter
DLOG(IN_GDP_R(-1)) – Log difference of Indian GDP, real at lag of 1 quarter
DLOG(IN_FOREX_RES(-1)) – Log difference of Indian Forex Reserves at lag of 1quarter
Predictors Impacting the Exchange rate after 2 Quarters
DLOG(US_S_EXPO_BOP(-2)), Log difference of Exports, services, BOP at lag of 2 quarters
DLOG(IN_GDP_R(-2)) – Log difference of Indian GDP, real at lag of 2 quarters
DLOG(US_GDP_R(-2)) – Log difference of GDP, real at lag of 2 quarters
Predictors Impacting the Exchange rate after 4 Quarters (1 year)
DLOG(GOLD_PRICE_USD(-4)) – Log difference of US Gold prices at lag of 4 quarters (approx. 1year)
Econometric model to predict USD/INR exchange rate has been finalized and can be easily used to check on the medium term and long term exchange rates to make much efficient business decisions. Also in the situations when there is any sudden change in the above mentioned indicators, business can hedge their risk by playing smartly beforehand rather than being exposed to the impact of these changes on the exchange rates.
Limitations & further research
This analysis and modeling exercise has achieved its objectives to a larger extent; however, certain unavoidable limitations such as time available for the research and analysis also limited the scope of the analysis.
The analysis was only performed on the selected economic indicators from Indian and American economies only hence prediction may be bit of skewed. Additionally, the analysis is just focused on the macro-economic factors and clearly focused on these factors and doesn’t take into account the micro-level factors which can put significant impact on the exchange rates during various intervals and thus can ultimately impact the long-term exchange rates to slighter extent and thus making our medium-term to long-term predictions wrong in either direction.
Again, there have not been many years since the currency started floating fully and hence provides less number of data points for the analysis and hence makes statistical analysis a bit difficulty to train the model for accurate predictions. Also, the quality of data published in India is not of that quality as it’s published in America due to lack of transparency and lack of dedicated data collection and research bodies. It acts as a major roadblock in making the analysis precise and impactful
This analysis has spurred many questions specifically around the time periods when the predicted values goes way different from the actual value of exchange rate and are not close and that needs to be further investigated. Further investigation is required to figure out the actions happened around that time-periods either in Indian or American market and those factors can be further studied for their significance to be entered into the model to fine-tune this prediction model.
References
Books
One Author
Basu, A. (1963), Consumer Price Index: Theory, Practice and Use in India, Modern Book Agency, Calcutta.
Two Authors
Singh, M. and Pandya, J.F. (1967), Government Publications of India, Metropolitan Book Co., Delhi.
Three Authors
Mote, V.L.; Malya, M. M. and Saha J. (1968), Tables for Capital Investment Analysis, Indian Institute of Management, Ahmedabad.
Edited Book
Basu, G. (ed.) (1962), Indian Tax Laws and Foreigners Having Investment in India or Having Business Connections in or with India, Oxford Book & Stationery, Calcutta.
Government Publication
Ministry of Law, Government of India (1960), The Copyright Act, 1957, The Manager of Publications, Delhi.
Journal Paper
Jain, S.K. (1967), World Class Manufacturing, International Journal of Operations Management, Vol. 6, No. 12, pp. 11-31.
pp. stands for page number.
Article in a Newspaper
Gandhi, V. P. (1968), Will the Budget Achieve Its Aims? Certain Doubts, The Economic Times, Mar. 8, pp. 5-6.
Conference Paper
Bhattacharyya, S.K. (1967), Control Techniques and Their Applicability, paper presented at the Ahmedabad Management Association, Ahmedabad, Nov. 22, pp. 11-17.