# Estimating with mean and standard deviation

This entry is part 17 of 23 in the series Numpy Strategies

Gravity waves. Aren’t they something! Today another distasteful finance post in which I try finding support and resistance. Actually I will just focus on resistance, since the procedure for support is similar. A new day, a new idea. This time the idea is that we can forecast a variable, by forecasting its mean, standard deviation and a correction factor. The mean and standard deviation will be calculated with a sliding exponential weights window. To determine the size of the window I will use the max lag given by a formula I found in the documentation of statsmodels ad_fuller. I don’t know where this formula comes from, but it looks reasonable. I hope that someone like Morgan Freeman can explain it (in a televisual way). Everything becomes clear when Morgan Freeman explains it. The following is quick and dirty code. Use with care I haven’t tested it properly yet. Since we are looking for resistance, I cheated by demanding a positive value for the correcting factor. For support I would require a negative value of course. Also there is some code to check after the fact how often the resistance holds for the prediction and if we cheat even more by adding a little bit to the resistance. I am not bothering with cross-validation here in the hope that statsmodels does something smart.

```def std_error(p): return np.sqrt(p - p**2)   def predict(a, lag): ar = AR(a) params = ar.fit(maxlag=lag).params   return ar.predict(params)   def print_stats(h, limit): hits = len(h[h &lt;= limit]) n = len(h)   ratio = hits*1.0/n print "Hits", hits, "Hit ratio", round(ratio, 2), "Std error", round(std_error(ratio),2)   lag = int(12 * (len(h)/100)**.25) ema = ewma(h, span=lag) pred_ema = predict(ema, lag)   devs = ewmstd(h, span=lag) pred_devs = predict(devs, lag)   fctr = (h - ema)/devs pred_fctr = predict(fctr, lag) pred_h = pred_ema[-1] + np.abs(pred_fctr[-1]) * pred_devs[-1] print pred_h   fit = pred_ema + np.abs(pred_fctr) * pred_devs y = h[lag:]   print_stats(h[lag:], fit) means = [] rest = np.abs(fit - y)   for i in xrange(len(rest)): slise = rest[:i] means.append(slise.mean() + slise.std())   print_stats(y, fit + means)```