Black Friday forecast: seasonality plus trend

An electronics retailer in Chicago sells much more in Q4 than in Q1, while the business also grows year after year. A plain line through the raw sales would be misleading, so the analyst first removes the seasonal pattern, fits the trend, and then puts the seasonality back to forecast the next cycle.

Task: line 1 is the season length m (for example 4 quarters). Line 2 holds the series (positive numbers); its length n is a multiple of m and at least 2m. Periods are numbered t = 1..n. Step 1: the overall mean M of all values. Step 2: for each position s = 0..m-1 in the cycle (period t has position (t-1) mod m) the seasonal index is mean of the values at that position / M. Step 3: deseasonalise each value, y_t = x_t / index[position]. Step 4: fit y = a + b * t by ordinary least squares with t = 1..n. Step 5: forecast the next m periods t = n+1..n+m as (a + b * t) * index[(t-1) mod m]. Print three lines: Indices: i0 i1 ... (3 decimals each), Trend: slope=B intercept=A (3 decimals) and Forecast: f1 f2 ... (2 decimals each). Print 0.000 instead of -0.000.