# VEEFX replies to: Statistics combined with system. Profitable? What do you think

Below article discusses combining statistics with trading. What is your opinion? Is this stochastic process a promising approach for statistical trading?
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Autoregressive Model

Autoregressive (AR) Model is a stochastic process representation for time series. In this model, the next variable of interest (e.g., next price) is modeled with linear combination of previous value(s) in a stochastic manner,
Attached Image
https://www.forexfactory.com/attachm…1&d=1445294734

where c is a constant, y_t is the variable of interest at time t and e_t is white noise. This stochastic process is usually referred to as an AR(p) model.

The trading algorithm is summarized below:
0. At the beginning of everyday’s candle (i.e., the open price of the day) the algorithm performs the following steps:
1. Compute the trend (e.g., the average) of the past N days’ close price, which is called P[] array.
2. Remove the trend from P[], store the result in D[] array.
3. Estimate the parameters of an AR(1) model.
4. Using D[] and the estimated model, perform Dickey-Fuller test. If D[] is stationary, go to (5) else go to (0)
5. Predict the next value of D[] (which is D[N+1]) using the estimated AR(1) model.
6. decision <- empty
6. If D[N+1]>D[N], then decision <- Buy, Close Sell else if D[N+1]<D[N], then decision <- Sell, Close Buy
7. Execute the decision.
8. Go to (0)

I developed an EA for testing this trading idea based on AR(1) model. Here is a backtest result from 2000 to 2015 on EURUSD:
Attached Image (click to enlarge)
https://www.forexfactory.com/attachm…1&d=1445296994

Discussion

This trading idea arises a set of questions such as:

1. Is this stochastic process (i.e., autoregressive model) a promising approach for statistical trading?
2. How can we improve the trade logic?
3. Does SL/TP settings for trades improve the results?
4. What if we increase p in AR(p) model?
5. Would it be more profitable if we use ARMA(p,q), ARIMA(p,d,q) and ARFIMA(p,d,q) models?
6. What about non-linear autoregressive models?

I am attaching the EA here. Hopefully any further improvement in the strategy would result in a newer version of the EA to test, and who knows, trading live!