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Thread: Assumptions of time series regression

  1. #1
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    noetsi's Avatar
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    Assumptions of time series regression

    I was wondering what the equivalent assumptions to Gauss Markov are for time series regression. Some are clearly different. Stationarity is not (as far as I know) an assumption of regression although it may be implicit in the assumption of equal error variance. Similarly time series normally does not assume that error terms are not serially correlated (they usually will be so you have to address that). And variables in time series are not iid until a significant period of time occurs in many cases.

    I could be wrong on all of that So what are the time series assumptions other than Stationarity and how do you test for them?

    In particular I am unclear if linearity and homoscedacity is part of the assumptions of multivariate time series.
    Last edited by noetsi; 07-12-2016 at 12:55 PM.
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    Re: Assumptions of time series regression


    as far as I know (ad as stated in different time series literature) homoscedacity is also an assumption in time series. And why should this not be the case? I mean time is also just a continuous variable. The only difference to other continuous variables (such as space) is that correlation makes only sense ''in backward direction'', but I don't see why this should lead to a neglection of homogeneity of variance over time.

    Regarding linearity: If we violate linearity, this leads to residual patterns, but we can deal with this by incorporating an appropriate autoregression structure. However, I think this is only the second choice if we are able to describe nonlinearities instead directly via nonlinear terms.

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    kiton's Avatar
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    Re: Assumptions of time series regression

    Hello there!

    From my econ class notes on the time-series, I have the following assumptions jotted down on the error term: zero mean, constant variance, no correlation with X, no autocorrelation (this is where, I believe, stationarity comes into play), and normal distribution. On the regressors, the following assumptions apply: Xi are fixed (non-random), Y is a linear function of Xi, and no multicollinearity is present. And finally, there is an assumption on betas -- Bi are constant, as otherwise there is a stochastic and/or dynamic process present.

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