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Unformatted text preview: 10.3 Time Series Thus Far Whereas cross sectional data needed 3 assumptions to make OLS unbiased, time series data needs only 2Although the third assumption is much strongerIf we omit a valid variable, we cause biased as seen and calculated in Chapter 3Now all that remains is to derive assumptions that allow us to test the significance of our OLS estimates Assumption TS.4 (Homoskedasticity) Conditional on X, the variance of u t is the same for all t: n. 1,2,..., t , ) ( )  ( 2 = = = σ t t u Var X u Var Assumption TS.4 Notesessentially, the variance of the error term cannot depend on X; it must be constantit is sufficient if: 1) u t and X are independent 2) Var (u t ) is constant over timeie: no trendingif TS.4 is violated we again have heteroskedasticityChapter 12 shows similar tests for Het as found in Chapter 8 Assumption TS.4 Violation Consider the regression: t t t t u politics tuition + + + = inflation 1 β β Unfortunately, tuition is often a political rather than an economic decision, leading to tuition freezes (=real tuition decreases) in an attempt to buy votesThis effect can span time periodsSince politics can affect the variability of tuition, this regression is heteroskedastic Assumption TS.5 (No Serial Correlation) Conditional on X, errors in two different time periods are uncorrelated: s t )  , ( ≠ 2200 = X u u Cor s t Assumption TS.5 Notes If we assume that X is nonrandom, TS.5 simplifies to: (10.12) ) , ( s t ≠ 2200 = s t u u CorIf this assumption is violated, we say that our time series errors suffer from AUTOCORRELATION, as they are correlated across timenote that TS.5 assumes nothing about intertemporal correlation among x variableswe didn’t need this assumption for cross sectional data as random sampling ensured no connection between error terms Assumption TS.5 Violation Take the regression: t t t t u exercise weight + + + = calories 1 β β If actual weight is unexpectedly high one time period (high fat intake), then u t >0, and weight can be expected to be high in subsequent periods (u t+1 >0) Likewise if weight is unexpectedly low one time period (liposuction), then u t <0, and weight can be expected to be low in subsequent periods (u t+1 <0) 10.3 Gauss Markov AssumptionsAssumptions TS.1 through TS. 5 are our Gauss Markov assumptions for time series dataThey allow us to estimate OLS varianceIf cross sectional data is not random, TS.1 through TS.5 can sometimes be used in cross sectional applicationswith these 5 properties in time series data, we see variance calculated and the Gauss Markov theorem holding the same as with...
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 Spring '09
 Priemaza
 Econometrics, Variance, time trend, time series

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