According to theory, the future market price can be analyzed and predicted by past trade information. But based on past to analyze and predict the future, there will be two distinct directions: one is the trend theory , this theory say that prices will be self-reinforcing, rising prices will increasingly rise and fall of prices is increasingly falling. Another is the mean reversion theory , this theory say that the price trend is just around the central value of random fluctuations, fell more will rise up more will fall.
According to the trend theory, people invented self-regression techniques (auto regression - AR). According to the mean reversion theory, people invented the technology moving average (moving average - MA). Of course, like Head & Shoulders shampoo combo ads, there are always some lazy people who want to once and for all the problems. So, we found the ARMA model.
ARMA model, also known as ARMA (p, q) model. The core idea is the current core as the name would suggest the entire model is to determine these two parameters p and q. Where, p determines the price we have to use several data lag period, and q determines the prediction error we have to use some lag period.
In simple terms, ARMA model does two things. First, based on trends in theory, historical data back to a current price forecasts, this forecast reflects autoregressive ideas. But this prediction is necessarily different, so ARMA model based on the prediction error of history but also a return to the current prediction error, this forecast reflects a weighted average of thinking. With price forecasts predict error correction plus, finally get a more precise theoretical prediction of the final price.
For example, if we use ARMA (2,2) model to predict the prediction Wanke stock regression parameters, the model is the AR-1 = AR-2 = 0.5, MA-1 = 0.6, MA-2 = 0.4. Over the past two days and is known to Wanke stock is 10 and 12, and the model is known in the last two days of the actual prediction error is 1 and 2, then the ARMA model can predict the day Wanke stock 0.5 * 10 * 12 + 0.5 + 0.6 + 0.4 * 2 * 1 = 12.4 yuan.
Compared to simple trend from simple regression model or time-based predictive models, ARMA model biggest advantage lies in a combination of theory and trends mean reversion theory, the theoretical accuracy will be higher.
But it is also the most difficult to grasp how to determine the parameters p and q. After all, as long as the parameters set, the remaining minor problems are software algorithms running. However, p and q How determined? Currently there is no absolute standard. Either from 1 to start a trial and error parameters, or to calculate the predicted price / lag phase error and the past few variables correlation value is larger, then the estimated values into a few large as p-value or the value of q model to see if significant. This parameter determines the process, quantitative analysts for the experience itself (or luck?) Puts bigger demands. Even found a significant build a ARMA model parameters are available, but also the parameters and timely adjustment according to market changes in the future.
Source: quantitative investment club
Further Reading:
1. a quantitative strategist Confessions (Good text strongly recommended)
2. classic quantitative trading strategies available in the market are here! (Source)
3. futures / stock data Daquan query (History / real-time / Tick / finance, etc.)
5. From the high-frequency trading to quantify, can not read five books
