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For the fitting and forecasting of time-series data on stock price, the most frequent model I have heard of is ARIMA. ARIMA is actually conducting a regression of stock prices and residuals of stock prices in the few days prior to the current date. ARCH model and its derivatives model variances on the data in the previous few days.

However, for the stock price, in particular, I believe most traders will not only rely on the stock prices in the past few days but also on the general trends in the past few months or even years. Therefore, the behaviors of traders should not be modeled fully based on stock prices in the past few days.

Is there a well-established model that considers stock prices not only in the past few days but also on the overall trend? Or if not, is there a reason why modeling only on the stock prices in the past few days is better than modeling on earlier data?

Thanks!

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Long story short no. Also, your question is too general in my opinion. Stock prices are not predictable according to the efficient market hypothesis. However there are many models one can try, they can include whatever you can think of from weather data to traffic data to the stock price 10 years ago of the company. There are momentum-based strategies that for example see the average gains from the whole industry over a long time horizon. The possibilities and combinations are endless, trying to find a good model to make you rich is, to say the least, a long shot.

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