CHAPTER 21: TIME SERIES ECONOMETRICS: SOME BASIC CONCEPTS

ü  Key Concepts

1.      Stochastic processes

2.      Stationary processes

3.      Purely random processes

4.      Nonstationary processes

5.      Integrated variables

6.      Random walk models

7.      Cointegration

8.      Deterministic and stochastic trends

9.      Unit root tests

ü  Stochastic Processes

A random or stochastic process is a collection of random variables ordered in time.

·         Stationary Stochastic Processes

A stochastic process is said to be stationary if its mean and variance are constant over time and the value of the covariance between the two time periods depends only on the distance or gap or lag between the two time periods and not the actual time at which the covariance is computed.

·         Nonstationary Stochastic Processes

2 Types of Random Walks

1.      Random walk without drift (no constant/intercept term)

2.      Random walk with drift (constant term is present)

ü  Trend Stationary (TS) and Difference Stationary (DS) Stochastic Processes

A TS time series has a deterministic trend, whereas a DS time series has a variable, or stochastic trend.

ü  Integrated Stochastic Processes

Properties of Integrated Series:

1.      If X_t      I(0) and Y_t      I(1), then Z_t = (X_t + Y_t) = I(1), that is, linear combination or sum of stationary and nonstationary time series is nonstationary.

2.      If X_t      I(d), then Z_t = (a + bX_t) = I(d), where a and b are constants.

3.      If Xt      I(d₁) and Y_t     I(d₂), then Z_t = (aX_t + bY_t) = I(d₂), where d₁ > d₂.

4.      If X_t      I(d) and Y_t      I(d), then Z_t = (aX_t + bY_t)      I(d*); d* is generally equal to d, but in some cases d*> d.

ü  The Phenomenon of Spurious Regression

Regression one time series variable on one or more time series variables often gave nonsensical or spurious results.

ü  Tests of Stationarity

1.      Graphical Analysis

2.      Autocorrelation Function (ACF) and Correlogram

ρ_k =     _k

             ₀

     = covariance at lag k

                Variance

ü  Cointegration: Regression of a Unit Root Time Series on Another Unit Time Series

Cointegration means that despite being individually nonstationary, a linear combination of two or more time series can be stationary.

·         Testing for Cointegration

-          Engle-Granger (EG) or Augmented Engle-Granger (AEG) Test

-          Cointegrating Regression Durbin-Watson (CRDW) Test

·         Cointegration and Error Correction Mechanism (ECM)

Error Correction Mechanism (ECM) – developed by Engle and Granger is ameans of reconciling the short-run behavior of an economic variable with its long-run behavior.