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Econometrical Time Series Analysis

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Published: 6th Dec 2019

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Behaviour of Macroeconomic Indicators Through Time Series Analysis and Granger Tests

Predicting the future outcomes of any indicator have had been considered one of the essential most analyses in any forecast measures, so its importance is parallel to no other forecast. The primary objective of any forecast is to identify the trends and patterns of changes in a set of variables to determine the possible future outcomes based on the previous trends the variable has been subject to as well as the influences on the behavioral pattern brought on the variable by other variables. Autocorrelation is the identification of weather the variable is self-correlated through the time continuum it exists in. This study was carried out to determine the significance of the autocorrelation technique used in economic forecast, and if it explained and predicted the future trends of major economic indicators depending on the past trends of the variables themselves. The second analysis examined is the Granger Causality test that identified the influences of other factors on the variables being tested.

Time series are sets of observations places and analyzed along a single linear dimension, such as time (Diebold, Kilian, & Nerlove, 2006). The main point of notion for any time series analysis in terms of forecast is deemed on the dependence of the same variable’s observations at different points in times in economic terms the use of economic indicators as these sets of observations. Another aspect to this is the other variables and factors influencing change in the depending variables. Granger causality tests indicated the developments in the individual economic variables that appeared to be systematically related to the overall economy and can thus serve as a leading indicator of its inter-temporal behavior. (Leigh, 1997).

Macroeconomic indicators are the set of parameters used to define the macro economical standing of an entity or a body for a given period of time (Che & Izani, 2004), based on this the economic indicators are considered as potential variable for the forecast analysis using a time based technique such as autocorrelation and a causal technique such as Granger Causality.

In Economics there are certain set of indicators that reflects the current state of the economy, a set that reflects the future state of the economy, and a set that reflects past economic activity (Che & Izani, 2004). These Indicators are regarded as the economic indicators of a country. Pakistan being one of the epicenters in the current day developing economies of the world and specifically the South East Asian region is extensively affected by the economical outcomes of the country in terms of future developments. Macroeconomic Indicators such as Population, GDP, Inflation, Interest Rates, FDI, Remittances, Monitory Policy, Imports and Imports are considered as the key indicator to evaluate the future outcomes of the economic development in Pakistan.

At macroeconomic level, the existing indicators are designed to provide extensive information about the main domains in which the policy intervention would be effective. The overall economy is therefore characterized, in terms of macroeconomic analysis, by output indicators, expressing the status of the economic activity (Zaman, 2007)

The subject matter of forecasting is uncertainty. Uncertainty means no clarity of time to come. In a state of uncertainty, establishments create determinations established on historical experience or even intuitive feeling. The decisions therefore taken through intuitive feeling are prejudicial to establishments. This takes scientific way of thinking to decision making. Forecasting is one such logical technique which assists establishments’ procedures in decision making in the state of uncertainty. Hence the application of Time Series frameworks in forecasting economic variables is significant in such future forecast; the technique applied in this paper are ACF and Grangers Causality Test.

Autocorrelation Function, originally named correlogram was devised by George Udny Yule. Autocorrelation is a linear quantity in which each variable is correlated based on the historical performance of that variable over time (Egan W. J., 2008). Similarly, an Individual Macroeconomic Variable not only captures information contained in past prices but also reflect fundamental macroeconomic variables that determine growth in Singapore (Leigh, 1997).

Problem Statement

The purpose of this study was to investigate the behavior of the macroeconomic indicators through the use of econometrical time series analysis such as Autocorrelation and Granger’s Causality techniques. To find out the forecast-ability of the Autocorrelation Function and Grangers Tests the study had engaged the Major Macroeconomic Indicators of Pakistan which are listed as follow.


Gross Domestic Product

Inflation rates

Foreign Exchange rates

Foreign Direct Investment

Money and Quasy (M2)



Balance of Payment

Various hypotheses had been tested on the forecast-ability of each variable to confirm upon the Forecast-ability of the complete autocorrelation function and Grangers Causality.

The Study is deemed to help analyst to predict the future standings of the current economic standings of the country through the use of Past records of those economic indicators. The study also identified the key future outcomes of Pakistan’s economic development in the variables studied in the research.

Outline of the Study

The main notion to the study was to identify the underlying principles of the Econometrical Time Series Analysis. The significance of the Forecast outcomes of the economic indicators (Population, GDP, Inflation rates, Exchange rates, Foreign Direct Investments, Monitory Policy, BOP, Imports and Exports) in regards to Pakistan’s Economy.

Forecasting the future outcomes of an economic indicator, it is important that proper forecasting tools were employed. Autocorrelation function had been used as a forecast indicator in the study to investigate the auto-correlative time series patterns and subsequently, Grangers Causality tests ensured the investigation of the existence of causality relationship between the Macroeconomic variables in Pakistan. Major Economic Indicator data of Pakistan of the past 28 years from 1980 to 2008 on an annual basis had been used in the study. Autocorrelation Function and other econometrical techniques were further used to investigate the outcome of the years to come.


Autocorrelation Hypothesis

H1: Autocorrelation in Population for current year forecasts the observations for forthcoming years

H2: Autocorrelation in GDP for current year forecasts the observations for forthcoming years

H3: Autocorrelation in Inflation for current year forecasts the observations for forthcoming years

H4: Autocorrelation in Exchange rates for current year forecasts the observations for forthcoming years

H5: Autocorrelation in FDI for current year forecasts the Future Insight for forthcoming years

H6: Autocorrelation in Money and Quasy for current year forecasts the Future Insight for forthcoming years

H7: Autocorrelation in Imports for current year forecasts the Future Insight for forthcoming years

H8: Autocorrelation in Exports for current year forecasts the Future Insight for forthcoming years

H9: Autocorrelation in Balance of Payment for current year forecasts the Future Insight for forthcoming years

Grangers Causality Test Hypothesis

H10: Granger’s Causality exists in Population

H11: Granger’s Causality exists in Gross Domestic Product

H12: Granger’s Causality exists in Inflation

H13: Granger’s Causality exists in Foreign Exchange rates

H14: Granger’s Causality exists in Foreign Direct Investment

H15: Granger’s Causality exists in M2 (Money and Quasy)

H16: Granger’s Causality exists in Present in Imports

H17: Granger’s Causality exists in Exports

H18: Granger’s Causality exists in Balance of Payment

Literature Review

The study of Time Series Analysis had been a subject of interest in multiple focuses throughout history from the early astronomical forecasting to the modern day economic and technological (Diebold, Kilian, & Nerlove, 2006). Time series had been an important source of analysis and forecast, Harmonic analysis had been considered one of the original most methods of forecasting time series overtime (Diebold, Kilian, & Nerlove, 2006).Time series analysis had evolved from various stages to the current automated analysis through econometrics. Automated discovery in science is a fairly recent phenomenon. It is commonly associated with the newfound capacity to collect, store and process vast amounts of data in extremely short periods of time. These capabilities come from sheer computational power and storage capability in conjunction with electronic communication, data processing and statistical analysis. Rapid information processing accelerates learning. It also enables algorithms to be implemented that automate judgments and scientific evaluations that would otherwise be made by human participants. The upshot is that empirical and experimental research could now be conducted in an automated fashion with much more limited human involvement than in the past (Phillips, 2004).

Forecasts had traditionally been made using structural econometric models. Concentration have been given on the univariate time series models known as auto regressing integrated moving average (ARIMA) models, which are primarily due to world of Box and Jenkins (1970). These models have been extensively used in practice for forecasting economic time series, inventory and sales modeling (Bajwa, Saeed, Saeed, & Zakria, 2000). The standard approach for building a model to forecast future values of a time series uses the analysis of the autocorrelation function and partial-autocorrelation function (Egan W. J., 2008).

Building a model to forecast the future values of a time series requires that we determine if there are any statistically significant autocorrelations in the data. The classic autoregressive integrated moving average (ARIMA) model of Box and Jenkins, as well as the autoregressive conditional heteroskedasticity (ARCH) family of models, use analysis of autocorrelation to guide the model building process. The Box-Jenkins model identification procedure involves tests of the statistical significance of the elements of the autocorrelation function and partial-autocorrelation function. These tests are used to determine if autoregressive and/or moving average patterns are present in the time series. (Egan W. J., 2008).

These statistical tests check if the observed autocorrelations exceed theoretical cutoffs. If they do, the autocorrelation at that time lag is deemed significant. Incorrect cutoffs would cause serious problems. Using incorrect cutoffs in the model building process will miss real autocorrelations or lead to the inclusion of false autocorrelations; either case will produce poor models giving misleading predictions. There are two possible causes of incorrect cutoffs which we will investigate in this paper (Egan W. J., 2008)

Autocorrelation (or serial correlation) is important in econometric analysis for when a time series shows significant autocorrelation, it is possible to represent it as a time series model (Levich & Rizzo, 1998). Economic time series are often characterized by positive autocorrelation. For macroeconomic data (such as gross domestic product, unemployment, housing starts, and so forth), such persistence is commonly associated with business cycle phenomenon and periods of expansion and recession (Levich & Rizzo, 1998).

While cross correlations give a first hint at the time structure of the indicators with respect to developments in industrial production they do not necessarily imply causation in the sense of Granger (1969). A more refined analysis to determine the lead of each indicator quantitatively can be performed with Granger causality tests. This test is used to see how much of the current variable Y can be explained by past values ues of Y and then to see whether adding lagged values of X can improve the explanation. Thus, X is said to Granger-cause Y if the X variable is statistically significant in the equation and therefore improves the forecast of Y (Hüfner & Schröder, 2002).

Many factors influence the economic growth process. These include, internal government policies, political stability, domestic capital formation, development of human capital, banking infrastructure, export policies, foreign direct investment, and foreign aid (Neelankavil, Stevans, & Roman Jr., 2009)

The variables analyzed are the economic Indicators. Economic indicators are usually used to forecast changing business cycle in an economy as they are descriptive and ex-ante time series data for forecasting economic or business conditions. They are useful for the study of cyclical expansions and contractions in business activities and have been grouped into 3 categories, namely leading, coincident and lagging indicators. The essential feature of the indicators system is the reference cycle, which is used to classify the categories of indicators (Che & Izani, 2004).

Leading economic indicators exhibit a business cycle by inclining to turn-down beforehand the down-cycle initiates and to turn-up afore the expansionary-cycle originates. Because of this characteristic they are important for financial markets, which are by nature forward-looking (Hüfner & Schröder, 2002).

Each and every variable in the said economic indicator have a different level of autocorrelation. Furthermore the variables are also correlated with other variables thus causing the illusion of being auto correlated while the change is being brought by another underlying variable. The high rate of inflation in Pakistan can be explained in terms of factors such as low rate of output growth, monetary expansion, higher dollar price of imports, exchange rate depreciation, increase in excise and sales taxes, and changes in administrative prices such as fuel prices, utility charges and procurement price of wheat (Bokhari & Feridun, 2006).

Amongst many of the economic variables, one of the most significant variables is Inflation (Bokhari & Feridun, 2006) and (Che & Izani, 2004). The inflationary impact of the depreciation of the exchange rate can similarly be regarded as an indirect effect of an escalation of money supply. Thus money supply would appear to be a key determinant of inflation in an economy (Bokhari & Feridun, 2006). Modeling and forecasting inflation is necessary for a number of reasons. It is important from the point of view of poverty alleviation and social justice. In addition, inflation is a regressive form of taxation and among the most vulnerable to the inflation tax are the poor and fixed income groups. Inflation also causes relative price distortion as some Prices adjust more slowly than others. These distortions cause efficiency losses and lower the productive base of the economy. (Bokhari & Feridun, 2006).

Apart from other Monitory Policy elements, Inflation however tends to be not entirely auto-correlated rather depends on other variables and economic indicators outcomes. Over the medium to long run – inflation is a monetary phenomenon, i.e. entirely determined by monetary policy. Over shorter horizons, however, various macroeconomic shocks, including variations in economic activity or production costs, will temporarily move inflation away from the central bank’s inflation objective (Dossche & Everaert, 2005).

Monitory Policy and Money supply in general, also influences the overall development of economy. It influences various factors involved in shaping the economy and henceforth in considered amongst the key indicators of economic forecast. Monetary policy decisions affect the economy with long and varying lags. It is therefore crucial to have an educated judgment about the economic conditions and outlook prevailing at the time (Fichtner, Rüffer, & Schnatz, 2009).

Interest rates are a considered a major financial indicator that influences decisions of final consumers, businesses users, financial institutions, professional investors and even legislative policymakers. Volatility in interest rates have had significant repercussions for the economy’s business-cycle and vital to explain financial growth and variations in economic policy (Radha & Thenmozhi, 2006).

The effects of FDI flows on economic development seem to have received the greatest attention. Researchers agree that FDI, by providing the much needed capital, the necessary foreign currency, and generating additional tax revenues from the foreign investors, plays a critical role in the growth dynamics of recipient countries (Neelankavil, Stevans, & Roman Jr., 2009).

FDI is also important factor and affects the economic volatility in both long-term and short-term manner. FDI is deemed as a positively contributing factor in the economic growth perspectives for both long and short term (Miankhel, Thangavelu, & Kalirajan, 2009). The inflow of foreign direct investment plays a crucial role in the dynamics of growth of receiving countries (Neelankavil, Stevans, & Roman Jr., 2009).The FDI-growth nexus is clearly identified by the neoclassical growth models. The neoclassical growth model considers technological progress and labor force as exogenous, and thus argues that FDI increases level of income only while it has no long run growth effect if it does not augment technology. Long run growth can only be increased through technological and population growth and if FDI positively influences technology, then it will be growth advancing (Miankhel, Thangavelu, & Kalirajan, 2009).

Besides FDI flows, research has also revealed other factors that have had reasonable effect on the economies of developing countries. These factors include the financial development of a country such as export promotion policies (Neelankavil, Stevans, & Roman Jr., 2009). Likewise the import Policies are also considered vital to the process in achieving Balance of Payment favorable to the countries development. There is the similar two-way causality discussion between exports -Imports and GDP (Miankhel, Thangavelu, & Kalirajan, 2009).

It is also important to highlight that the interaction between these variables is complex and each variable (GDP, exports and FDI) has a plausible theoretical foundation to affect the other variables. Without knowing the direction and pattern of mechanisms among these variables can hamper effective policy to promote economic growth. Therefore it is important to investigate the relationship between these variables to correctly formulate policies in respective countries (Miankhel, Thangavelu, & Kalirajan, 2009). Similarly Monitory policy, interest rates and inflation influences the financial side of the country’s economic growth and effect the GDP in financial terms (Bokhari & Feridun, 2006) and (Che & Izani, 2004).

The measure of the economic output serves for various purposes: analysis of the overall economic activity over past periods, forecast of future trends, international comparisons, etc. (Zaman, 2007).

The variables being a part of macroeconomic environment of a country also based some causality over each other. The causal relationships between demographic and economic variables have been empirically examined in various researches. The identification of the relationships between demographic variables and socio-economic ones is fundamental to be able to asses and be ready to confront the consequences of these structural demographic changes in future years (Climent & Meneu, 2003).

Although many aggregate econometric studies have been conducted with FDI as a dependent variable, a broad consensus on the major determinants of FDI has been elusive. It had also noted to have substantial discrepancies in the basic macroeconomic variables that characterize an economy. (Singh & Jun, 1995). Similarly, Forecasting inflation is vital to adjust its monetary policy to control inflation (Moriyama & Naseer, 2009). Research also shows an existing but weak two-way causality between broad money (M2), Exchange Rate and inflation. Thus, Money growth and foreign exchange rate change to inflation with some lags, suggesting the causality is not strong (Moriyama & Naseer, 2009). Also, money (M2) and interest rates have information content for future movements in real GDP beyond that contained in past values of GDP itself. This relationship only establishes itself with a fairly long lag. The finding suggests the possibility of making use of the money-income relationship for forecasting purposes (Feridun , 2006).

Any economy has a certain degree of openness towards the rest of the world. The economic links are carried out through two principal channels: the exchange of goods and services, respectively the inflow and outflow of capital. (Zaman, 2007). And the Balance of Payment serves for recording commercial and financial exchanges (Zaman, 2007). Many transactions are operated in practice in different currencies; the conversion is done by using a specific exchange rate of the domestic currency, expressed in units of a foreign currency (Zaman, 2007).

Research Methods

Methods of Data Collection

The main source of data collection is through the secondary source. Data of major economic indicators of Pakistan for 28 years (from 1980 – 2008) had been collected through various websites. Major part of which had been collected from the World Bank database, CIA Fact File, Index Mundi and Federal burro of Statistics Pakistan.

Following are the economic indicators that are collected and studied upon;


Current Gross Domestic Product

Inflation rates (based on CPI)

Foreign Exchange rates (PKR against US$)

Foreign Direct Investment

Money and Quasy (M2)



Balance of Payment (Current Account)

Sample Size

Annual observations of major economic indicators of Pakistan (Population, GDP, Inflation rates, Foreign Direct Investments, Monitory Policy, BOP, Imports and Exports) for 28 years starting from 1980 to 2008 had been included in the sample size. This is considered a sufficient sample size for running econometric and time series tests for accurate results.


Autocorrelation Function

The major tests applied in the study are based on the econometric principle of time series forecast i.e. Autocorrelation Function. Autocorrelation Function is important in econometric analysis for when a time series shows significant autocorrelation, it is possible to represent it as a time series model (Levich & Rizzo, 1998)

Autocorrelation is defined as “correlation between members of series of observations ordered in time [as in time series data] or space [as in cross-sectional data].” (Gujarati, 2002). The Autocorrelation is calculated using the following;

Where, while,


is the sample mean of the time series, N is the number of observations, t is the index of the observation, and k is the lag (Egan W. J., 2008).

Granger Causality Test

The concept of Granger causality, by which precedence in time series is actually investigated, was based on the idea that a cause cannot come after its effect. More precisely, variable X is said to Granger-cause another variable, Y, if the future value of Y ( yt+1 ) is conditional on the past values of X ( xt-1, xt-2, … , x0 ) and thus the history of X is likely to help predict Y (Kónya, 2000).

The procedure used in Granger Causality Test in this paper is direct approach. It does not rely so heavily on pre-testing, though some knowledge of the maximum order of integration and of the lag structure is still required. We start with the indirect approach, and thereafter we employ the direct approach (Kónya, 2000).

Analysis on the variable was considered in terms of unilateral terms only, that are the Variable ‘X’ Granger-causality on Variable ‘Y’ (Kónya, 2000).

Empirical Findings

Grangers Causality Test

Before conducting the autocorrelation tests, granger’s causality test is used on the assigned variables to check the casual relation between the variables amongst each other’s. This had provided with the evidence of a unilateral or bilateral relation between variables used in the study. Following results are generated using e-views.

Based on the granger’s causality test, many of the variables were found with either unilateral or bilateral relationships, this information would thus define the influence of one macroeconomic factor over the other dependent on the variable.

The Significance level for Granger Causality acceptance used in the research was 8%. Thereafter the granger model was based on keeping a 3.5 F-statistic threshold to determine the casual relationship between variables. That in any variable with a higher than 3.5 F-statistic in regards to the other variable is considered a casual relation of that variable against the variable on which the test is being run.

Table 1.1 Pairwise Granger Causality Test

Pairwise Granger Causality Tests

Sample: 1980 2008

Lags: 2

Null Hypothesis:



EXCHANGE does not Granger Cause BOP



BOP does not Granger Cause EXCHANGE



BOP does not Granger Cause EXPORTS



EXPORTS does not Granger Cause BOP



FDI does not Granger Cause BOP



BOP does not Granger Cause FDI



BOP does not Granger Cause GDP



Ho: Accepted

IMPORTS does not Granger Cause BOP



BOP does not Granger Cause IMPORTS



INFLATIO does not Granger Cause BOP



Ho: Accepted

EXPORTS does not Granger Cause EXCHANGE



EXCHANGE does not Granger Cause EXPORTS



FDI does not Granger Cause EXCHANGE



EXCHANGE does not Granger Cause FDI



GDP does not Granger Cause EXCHANGE



EXCHANGE does not Granger Cause IMPORTS



INFLATIO does not Granger Cause EXCHANGE



Ho: Accepted

EXCHANGE does not Granger Cause INFLATIO



Ho: Accepted

M2 does not Granger Cause EXCHANGE



Ho: Accepted

EXCHANGE does not Granger Cause M2



Ho: Accepted

FDI does not Granger Cause EXPORTS



Ho: Accepted

EXPORTS does not Granger Cause FDI



GDP does not Granger Cause EXPORTS



Ho: Accepted

EXPORTS does not Granger Cause GDP



Ho: Accepted

INFLATIO does not Granger Cause EXPORTS



EXPORTS does not Granger Cause INFLATIO



Ho: Accepted

M2 does not Granger Cause EXPORTS



Ho: Rejected

EXPORTS does not Granger Cause M2



POPULATI does not Granger Cause EXPORTS



GDP does not Granger Cause FDI



FDI does not Granger Cause GDP



Ho: Accepted

FDI does not Granger Cause IMPORTS



Ho: Accepted

FDI does not Granger Cause INFLATIO



POPULATI does not Granger Cause FDI



IMPORTS does not Granger Cause GDP



Ho: Accepted

GDP does not Granger Cause IMPORTS



INFLATIO does not Granger Cause GDP



Ho: Accepted

GDP does not Granger Cause INFLATIO



Ho: Accepted

GDP does not Granger Cause M2



Ho: Accepted

POPULATI does not Granger Cause GDP



Ho: Accepted

GDP does not Granger Cause POPULATI



INFLATIO does not Granger Cause IMPORTS



Ho: Accepted

IMPORTS does not Granger Cause INFLATIO



POPULATI does not Granger Cause IMPORTS



M2 does not Granger Cause INFLATIO



Ho: Accepted

INFLATIO does not Granger Cause M2



Ho: Accepted

POPULATI does not Granger Cause INFLATIO



POPULATI does not Granger Cause M2



Ho: Accepted

M2 does not Granger Cause POPULATI




Trends regarding population are mostly unilateral. Some of the major effects were noted in Foreign Direct Investment and Inflation of the country. This suggests that Population had a strong causal relationship over FDI and Inflation and with the increase in Population, the FDI and Inflation would also increase. This also complies with the historical evidences on the topic (Climent & Meneu, 2003).

Population was also found having a significant casual relation with Inflation suggesting that the Rise in Inflation is caused by the Rise in Population (Climent & Meneu, 2003).

Gross Domestic Product

GPD had strong casual relation with Population and FDI which suggested that GDP influences changes in Population through disperse or immigration. Some historical evidences also suggest that a countries fertility rate is positively related to the GDP of the country in long run (Climent & Meneu, 2003). Also there is a strong relation with FDI which indicates that GDP may influence the FDI coming in the country (Singh & Jun, 1995)

GDP also had significant causal relations with Imports and Exchange Rates. This suggest that with the rise in the population, demand for Imports would rise and thus effecting a change in both Imports and Exchange Rates (Kónya, 2000).

Exchange Rates

An exchange rate of the country was mainly affecting the variables concerned with foreign dealing and trades. BOP and Exports had a highly significant relation with Exchange rate suggesting a strong influence in FDI and Exports is caused by Exchange Rates of the Host Country (Staiger & Sykes, 2008). Other than this Imports and FDI were also very close to the required threshold of acceptance employed in the study.

Balance of Payment

Balance of Payment only had significant causal relations with foreign trade. FDI, Exchange Rate, Exports and Imports had a significant causal relation indicating the influence of Balance of Payment over the variable. Economically the results have coincided with the historical data available on the variable. (Blanchard, Giavazzi, & Sa, 2005)


Exports had strong casual relations with

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