Spurious regression is generated when we regress time series data that are non-stationary. So is it possible to time lag the variable to further find a higher correlation?
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Taking lagged non-stationary variable as a covariate in a regression model will result in spurious model as well, which will output an optimistically high biased value of t-statistic and r squared. This is because non-stationary time-series have very long memory as could be illustrated by an acf function plot.
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$\begingroup$ What model can you recommend in these analysis of non-stationary variables so spurious model would be omitted? I am analyzing a commodity price and a stock price. $\endgroup$– chidoriCommented Nov 2, 2017 at 10:06
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$\begingroup$ @chidori, a good choice is to take first differences of the time-series (returns). I specifically recommend log(xt) - log(xt-1) when it comes to stock data, which are unstationary in terms of variance of the returns. $\endgroup$ Commented Nov 2, 2017 at 10:31
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$\begingroup$ So according to my research, ways to omit spurious results is to make the time series data stationary. If it exhibits a random walk, I need to use differencing and when it has a deterministic trend, I can detrend it. But if it fails, I'll analyze the returns instead (which what you have said). So when I examine the returns, do I assume it to be stationary? And what is the difference in normal returns and log(xt) - log(xt-1) and if it is unstationary, how do I correlate it? $\endgroup$– chidoriCommented Nov 2, 2017 at 10:39
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$\begingroup$ @chidori, it is not necessary to detrend by substracting a trend model. You can take differences and the trend goes away. However, you can try to detrend, but then you don't take differences. log(xt) - log(xt-1) helps a lot when your returns are not stationary in variance. $\endgroup$ Commented Nov 2, 2017 at 10:44
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$\begingroup$ What's the best correlation method for log returns? $\endgroup$– chidoriCommented Nov 2, 2017 at 10:53