Download presentation

1
**Regression with Time Series Data**

Judge et al Chapter 15 and 16

2
Distributed Lag

3
**Polynomial distributed lag**

4
**Estimating a polynomial distributed lag**

5
Geometric Lag Impact Multiplier: change in yt when xt changes by one unit: If change in xt is sustained for another period: Long-run multiplier:

6
**The Koyck Transformation**

7
**Autoregressive distributed lag**

ARDL(1,1) ARDL(p,q) Represents an infinite distributed lag with weights: Approximates an infinite lag of any shape when p and q are large.

8
Stationarity The usual properties of the least squares estimator in a regression using time series data depend on the assumption that the variables involved are stationary stochastic processes. A series is stationary if its mean and variance are constant over time, and the covariance between two values depends only on the length of time separating the two values

9
Stationary Processes

10
**Non-stationary processes**

11
**Non-stationary processes with drift**

12
**Summary of time series processes**

Random walk Random walk with drift Deterministic trend

13
**Trends Stochastic trend Deterministic trend Random walk**

Series has a unit root Series is integrated I(1) Can be made stationary only by first differencing Deterministic trend Series can be made stationary either by first differencing or by subtracting a deterministic trend.

14
Real data

15
Spurious correlation Two random walks we observed earlier.

16
**Spurious regression R2 0.7495 D-W 0.0305 Variable DF B Value Std Error**

T ratio Approx prob Intercept 1 0.5429 26.162 0.0001 RW2 R D-W

17
**Checking/testing for stationarity**

Correlogram Shows partial correlation observations at increasing intervals. If stationary these die away. Box-Pierce Ljung-Box Unit root tests

18
**Unit root test If || < 1, then the AR(1) process is stationary.**

We can test for nonstationarity by testing the null hypothesis that = 1 against the alternative that , or simply < 1.

19
**Dickey Fuller Tests Allow for a number of possible models**

Drift Deterministic trend Account for serial correlation Drift Drift against deterministic trend Adjusting for serial correlation (ADF)

20
**Critical values Table 16.4 Critical Values for the Dickey-Fuller Test**

Model 1% 5% 10% 2.56 1.94 1.62 3.43 2.86 2.57 3.96 3.41 3.13 Standard critical values 2.33 1.65 1.28

21
**Example of a Dickey Fuller Test**

22
Cointegration In general non-stationary variables should not be used in regression. In general a linear combination of I(1) series, eg: is I(1). If et is I(0) xt and yt are cointegrated and the regression is not spurious et can be interpreted as the error in a long-run equilibrium.

23
**Example of a cointegration test**

Model 1% 5% 10% 3.90 3.34 3.04

Similar presentations

OK

Review and Summary Box-Jenkins models Stationary Time series AR(p), MA(q), ARMA(p,q)

Review and Summary Box-Jenkins models Stationary Time series AR(p), MA(q), ARMA(p,q)

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google