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I see many online blogs that use Linear Regression to predict future stock price. I too have done this and my x variable is time elapsed.

But I have been advised this problem is better suited for Time Series problem instead of Linear Regression. I want to understand why and what is the difference between say ARIMA and Linear Regression in the context of predicting future stock prices based on historical data. e.g. date and closing price.

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  • $\begingroup$ I see that you do not accept the answer and not ask clarifications, nor give opinions. What do you think? $\endgroup$ – markowitz Dec 5 '20 at 20:21
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I want to understand why and what is the difference between say ARIMA and Linear Regression in the context of predicting future stock prices based on historical data. e.g. date and closing price.

Start to say that we can see ARIMAs as models builded for non stationary/integrated series and we can see ARMA as a restriction on stationaries one. After differentiation we can reduce integrated in non integrated series, so after this passage we can work with ARMA.

Now, limiting ourselves on the comparison between ARMA and linear regression we can say that them are strongly related, in some extent we can conflate them. Suffice to keep in mind that under usual condition (stationarity, invertibility) an ARMA process can be represented as a pure AR one; pure autoregressive.

Regarding the stocks, keep in mind that predict price is easy but predict return is challenging. For (log)price is usual the Random Walk assumption that in ARIMA term is ARIMA(0,1,0); it imply an ARMA(0,0), white noise, for the (log)return.

Read here too: Forecasting Prices vs Returns by Deep Learning

In any case (price/return) insert a time trend in regression is not a good idea.

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    $\begingroup$ It is difficult to see how linear regression of a response against time (as described in the question) might be "strongly related" to or even conflated with ARMA/ARIMA modeling. This assertion might even be misleading unless the relationship is clearly spelled out. Could you elaborate on that in your answer? $\endgroup$ – whuber Dec 2 '20 at 18:08
  • $\begingroup$ I can try, give me some minutes $\endgroup$ – markowitz Dec 2 '20 at 18:11
  • $\begingroup$ I skipped the problem of time trend because it seem me not a core point. $\endgroup$ – markowitz Dec 2 '20 at 18:25
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    $\begingroup$ I think that is the entire point of this question. $\endgroup$ – whuber Dec 2 '20 at 19:19
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    $\begingroup$ It's not a matter of what you or I might think: the question quite clearly and explicitly states "use Linear Regression to predict future stock price. I too have done this and my x variable is time elapsed." There's no need to wait to know the OP's opinion! $\endgroup$ – whuber Dec 2 '20 at 20:17

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