This chapter’s objectives are to: Introduce intervention analysis and transfer function analysis, show that transfer function analysis can be a very effective tool for forecasting and hypothesis testing when it is known that there is no feedback from the dependent to the so-called independent variable, | Chapter 5 Applied Econometric Time Series 4th ed. Walter Enders 1 1 2 An Intervention Model 3 Consider the model used in Enders, Sandler, and Cauley (1990) to study the impact of metal detector technology on the number of skyjacking incidents: yt = a0 + a1yt–1 + c0zt + et, a1 < 1 where zt is the intervention (or dummy) variable that takes on the value of zero prior to 1973Q1 and unity beginning in 1973Q1 and et is a white-noise disturbance. In terms of the notation in Chapter 4, zt is the level shift dummy variable DL. Steps in an Intervention Model STEP 1: Use the longest data span (., either the pre- or the postintervention observations) to find a plausible set of ARIMA models. You can use the Perron (1989) test for structural change discussed in Chapter 4. STEP 2: Estimate the various models over the entire sample period, including the effect of the intervention. STEP 3: Perform diagnostic checks of the estimated equations. 4 5 6 Table : Metal Detectors and Skyjackings 7 Pre-Intervention Mean a1 Impact Effect (c0) Long-Run Effect Transnational {TSt} () () () . Domestic {DSt} () ( ) Other Skyjackings {OSt} () () ( ) Notes: 1. t-statistics are in parentheses 2. The long-run effect is calculated as c0/(1 a1) ADLs and Transfer Functions 8 Transfer Functions yt = a0 + A(L)yt–1 + C(L)zt + B(L)et where A(L), B(L), and C(L) are polynomials in the lag operator L. In a typical transfer function analysis, the researcher will collect data on the endogenous variable {yt} and on the exogenous variable {zt}. The goal is to estimate the parameter a0 and the parameters of the polynomials A(L), B(L), and C(L). Unlike an intervention model,{zt} is not constrained to have a particular deterministic time path. It is critical to note that transfer function analysis assumes that {zt} is an exogenous process that evolves independently of the {yt} sequence. 9 The CCVF The . | Chapter 5 Applied Econometric Time Series 4th ed. Walter Enders 1 1 2 An Intervention Model 3 Consider the model used in Enders, Sandler, and Cauley (1990) to study the impact of metal detector technology on the number of skyjacking incidents: yt = a0 + a1yt–1 + c0zt + et, a1 < 1 where zt is the intervention (or dummy) variable that takes on the value of zero prior to 1973Q1 and unity beginning in 1973Q1 and et is a white-noise disturbance. In terms of the notation in Chapter 4, zt is the level shift dummy variable DL. Steps in an Intervention Model STEP 1: Use the longest data span (., either the pre- or the postintervention observations) to find a plausible set of ARIMA models. You can use the Perron (1989) test for structural change discussed in Chapter 4. STEP 2: Estimate the various models over the entire sample period, including the effect of the intervention. STEP 3: Perform diagnostic checks of the estimated equations. 4 5 6 Table : Metal Detectors and Skyjackings 7 .
