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I've heard that stock prices are random. But I know if the price is 15 at one tick, the next price has a range that hovers around 15 because it won't randomly hit 15,000,000 in the next tick.

Fist, how could I go about finding the answer to that question myself? I was thinking of downloading historical tick data on Apple Inc. and running this regression in Stata

reg price time

then doing a newey test. Would I need to include volume? And what lag is normally used for this?

Second, to find an answer about stocks in general, would I have to look at every stock? Or is a random sample good enough?

I looked at some research from the top google results of "is there autocorrelation in stock prices". But it was a little over my head. What I managed to gather is that at least for stock returns yes, there is, in large diversified portfolios. Any further light and knowledge is appreciated.

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    $\begingroup$ You don't really need to run regressions. Your friends are the time-domain tools of time-series analysis called the autocorrelation function and partial autocorrelation function. Take a look at those for the stock prices in levels and you'll probably see a slow declining ACF and single spike in PACF. After differencing, you'll see white-noise. At least, that's what you should expect. There are many papers on the related issue of stock market efficiency and how to test this. Pretty sure John Cochrane's Asset Pricing book contains a list of tests or check anything by Eugeme Fama. $\endgroup$ – Graeme Walsh Mar 27 '16 at 0:56
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Stock prices follow a random walk process, usually we include a drift term to account for the somewhat prolonged upward/downward drifts. This is basically an AR(p) process, p being the lag order. For instance AR(1) with drift is $X_t=\delta+\beta X_{t-1}+u_t$ where $\beta = 1$. Try testing this model for unit root using ADF test in stata. One lag is enough. You should fail to reject the unit root for an evidence of autocorrelation in the prices. Stock returns are not autocorrelated, they usually follow a stationary process if you take sufficiently long sample.

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  • $\begingroup$ If you assume (log) price follows a random walk (using any reasonable definition of random walk), then (log) returns are necessarily uncorrelated. (Stationarity has nothing to do with sample size.) $\endgroup$ – Michael Mar 29 '16 at 8:05

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