I am trying to determine the best method for a temporal regression model. For a give time period there are two outcomes. I want a model that gives the probability of one of the two outcomes based upon a dataset. One of the independent variables in the dataset if time. At time 0 we should be 100% sure which of the two outcomes occurred.
Here is an example. Let's say that I have some stock data at different times throughout the day. At the closing bell the stock can either be UP or DOWN on the day. Based upon data throughout the day I want to know the probability that the stock will be UP at the closing bell. Of course, at the closing bell (time = 0), I am 100% sure if the stock is up or down.
Hello Michael,
The classical approach to the problem you describe is time series analysis. The classical text is Box and Jenkins (1976). The basic idea is to model a time series as either an autoregressive or moving average model. No doubt there are any number of unbelievably sophisticated time series analytic techniques, developed since Box and Jenkins. This would include Bayesian approaches. These combine data up to a point in time with prior probabilities to obtain a posterior (after the fact) probability.
Good luck,
David S
Dear Michael
1. Linear regression model/analysis is a technique used to predict the value of one quantitative variable by using its relationship with one or more additional quantitative variables.
The simple/multiple linear regression model is a mathematical way of stating the statistical relationship that exists between two/more than two variables.
2. Regarding your data, since the data is based on time, I suggest to develop time series analysis. It may be noted here that the
time series consists of statistical data which are collected, recorded or observed over successive increments of time.
Regards,
Zuhair
Hello MIchael,
Time series analysis takes into account the fact that sequential data is autocorrelated--examples are stocks and the weather. There are glm models that take into account autocorrelated data such as generalized estimating equations (GEE package in R) , but they are way more complicated than a glm model that assumes uncorrelated explanatory variables with normal errors. The GEE package in R allows binomial response (yes/no) which would be appropriate to your question. So take your pick--GEE or time series analysis. Either way, you need to deal with the autocorrelation that comes with time series.
~David S
Hello Matthew,
As an environmental scientist I understand what causes autocorrelation in the weather. Autocorrelation in stock prices is well documented, and if I understood what drives it, I could make a lot of money on the market. Here is an example of speculation on the topic.
Momentum and Autocorrelation in Stock Returns (Digest Summary)
Jonathan Lewellen
Review of Financial Studies, Vol. 15, No. 2 (Special 2002): 533-563 Summarized by Robert A. McLean, CFAhttps://doi.org/10.2469/dig.v32.n3.1130
Abstract
Momentum in stock prices is a persistent but unexplained phenomenon. The author examines momentum in returns to portfolios sorted by industry, company size, and book-to-market ratio. His results suggest that momentum is the result of excess covariance among stock prices.
Momentum in stock prices is a persistent but puzzling phenomenon. The author shows that momentum is not limited to individual stocks but is also observed in industry, book-to-market, and company-size portfolios. He argues that momentum is the result of excess covariance among stocks.
Momentum is widely observed in stock prices. Winners tend to remain winners, and losers tend to remain losers. This phenomenon suggests that the stock market may not be efficient, even in the weak sense. Most analysts attribute momentum to company-specific returns (Jagadeesh and Titman, Review of Financial Studies, 1995). A few scholars have developed behavioral models for the underreaction of stock prices to news (Barberis, Sheifer, and Vishny, Journal of Financial Economics, 1998)
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Returning to the initial query, autocorrelation is the norm for stock prices, which points at taking it into consideration in any attempt to model it. ARIMA models consider autocorrelation as a result inertia (as above, momentum) and autocorrelation as the result of event effects. And so to your query, autocorrelation can result from either momentum or from external events, and be modeled as such.
Taking it the next step, I am certain that a merely descriptive model could be found for price at the end of the day, as per the query that initiated this discussion. I am skeptical that a model that could *predict* stock prices at the end of the day could be found.
~David S
I am suggestion to used generalized linear mixed model or Time series
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