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I am trying to determine which quantitative model to try and build a predictive model for the next day's closing price for all the S&P stocks based on their bar for that particular day. However, I am not sure how to think about this.

I've previously used historical data to try and predict closing prices, which would be far easier. Over here, I am thinking I can assume the stocks follow a lognormal distribution and I can then try and determine the parameters of this distribution based off of the bar and eventually use a Monte Carlo Simulation, where I randomly sample from this Lognormal to get the closing price for each stock. Does this sound okay?

Edit: I've rethought the problem and now approaching it as follows:

I am trying to find closing price using the equation below: $ClosingPrice_{t}=alpha1∗OpeningPrice_{t}+alpha2∗HighPrice_{t}+alpha3∗LowPrice_{t}$

where each of the variables opening price, the Highest value and lowest value are modelled by their own ARIMA Time-Series, as is commonly used to model stock prices. However, for the model to determine closing price I plan on using a Ride Regression as I suspect there will be multicollinearity between some of these variables.

Does this model make sense?

Thanks

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    $\begingroup$ What do you mean by "bar" here? $\endgroup$ – user32416 Oct 21 '15 at 19:23
  • $\begingroup$ @user32416 Its the open and close in a candlestick chart. $\endgroup$ – Jojo Oct 22 '15 at 1:07
  • $\begingroup$ I'll offer a partial answer. This sounds more like "technical analysis" than a quantitative approach. There's practically no solid fundamental economic nor financial reason why the "bar" would have any predictive power for the price tomorrow (let alone its closing price). Your lognormal estimation is very against the empirical evidence that asset returns do not follow a Gaussian form. So in one sense, yes, of course you can do what you're proposing (nobody can stop you from doing that). But I question how good would your results be. $\endgroup$ – user32416 Oct 22 '15 at 17:11
  • $\begingroup$ And also even if you do all that, I'm not sure how exactly does the Monte Carlo from an estimated lognormal random variable will help you in pinning down the "exact" (or somewhere near there) of the next day closing price. You do your Monte Carlo for say 10^10 times, and you'll get a bunch of realizations. Then what do you do? You take the sample mean of this? You'd just effectively get back your estimated mean that you'd used from the historical data (i.e. Law of Large Numbers). $\endgroup$ – user32416 Oct 22 '15 at 17:16
  • $\begingroup$ @Jojo I am not sure what you are doing. I guess with bar you mean candlesticks. It is unclear to me how you would forecast the closing price of the day $t+1$ from the candlestick at $t$. What is your model about? As user32416 pointed out your approach sounds like technical analysis. Furthermore, why are you assuming a log norm distribution? Have you tried to plot your model output f.ex. as a simple histogram? Please clarify before we can help you in detail! $\endgroup$ – Kare Oct 22 '15 at 18:04
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Yes sounds OK!

Try also stochastic volatility models like ARCH or GARCH.

Another way of forecasting would be using a Mandelbrotian fractal.

Other solution: Markov Chains

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    $\begingroup$ This is not specific nor helpful. And furthermore, it sounds nothing more than a bunch of buzzwords thrown together. $\endgroup$ – user32416 Oct 22 '15 at 17:08

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