# Unable to perform Holt-Winters forecasting on time series data

I am trying to perform a Holt-Winters forecasting for future dates in Python. There is a working code but it only predicts one point ahead so at the end of the series, I only one more point for the HoltWinters, I would like to modify this code and add 3 more months to the forecasted values.

I've been trying to figure this out and not able to solve it. I'd really appreciate any insight or what I am doing wrong:

Series data looks like this, first value is the actual data point and second is the time in epoch format:

[[111318489540.15584, 1419872032], [111319184415.82709, 1419958432], [111319382979.16595, 1420044832], [111318808170.7551, 1420131232], [111318903144.42294, 1420217632]


This is the working code for one point forecasting:

def holtWintersAnalysis(series):
alpha = gamma = 0.1
beta = 0.0035
# season is currently one day
season_length = (30*24*60*60) / series.step
intercept = 0
slope = 0
pred = 0
intercepts = list()
slopes = list()
seasonals = list()
predictions = list()
deviations = list()

def getLastSeasonal(i):
j = i - season_length
if j >= 0:
return seasonals[j]
return 0

def getLastDeviation(i):
j = i - season_length
if j >= 0:
return deviations[j]
return 0

last_seasonal = 0
last_seasonal_dev = 0
next_last_seasonal = 0
next_pred = None

for i,actual in enumerate(series):
if actual is None:
# missing input values break all the math
# do the best we can and move on
intercepts.append(None)
slopes.append(0)
seasonals.append(0)
predictions.append(next_pred)
deviations.append(0)
next_pred = None
continue

if i == 0:
last_intercept = actual
last_slope = 0
# seed the first prediction as the first actual
prediction = actual
else:
last_intercept = intercepts[-1]
last_slope = slopes[-1]
if last_intercept is None:
last_intercept = actual
prediction = next_pred

last_seasonal = getLastSeasonal(i)
next_last_seasonal = getLastSeasonal(i+1)
last_seasonal_dev = getLastDeviation(i)

intercept = holtWintersIntercept(alpha,actual,last_seasonal
,last_intercept,last_slope)
slope = holtWintersSlope(beta,intercept,last_intercept,last_slope)
seasonal = holtWintersSeasonal(gamma,actual,intercept,last_seasonal)
next_pred = intercept + slope + next_last_seasonal
deviation = holtWintersDeviation(gamma,actual,prediction,last_seasonal_dev)

intercepts.append(intercept)
slopes.append(slope)
seasonals.append(seasonal)
predictions.append(prediction)
deviations.append(deviation)

# make the new forecast series
forecastName = "holtWintersForecast(%s)" % series.name
forecastSeries = TimeSeries(forecastName, series.start, series.end
, series.step, predictions)
forecastSeries.pathExpression = forecastName

# make the new deviation series
deviationName = "holtWintersDeviation(%s)" % series.name
deviationSeries = TimeSeries(deviationName, series.start, series.end
, series.step, deviations)
deviationSeries.pathExpression = deviationName

results = { 'predictions': forecastSeries
, 'deviations': deviationSeries
, 'intercepts': intercepts
, 'slopes': slopes
, 'seasonals': seasonals
}
return results


It looks like it is looking at the data and performing holtWinters algo and appending values to a list called:

predictions


The next after this loop:

for i,actual in enumerate(series):


...

## I put these lines to

 ##remove non numeric values (e.g. from the list)
predictions=filter(None,predictions)
#retrieve the last predicted value
last_pred=predictions[-1]
#remove non numeric values from the slopes list
slopes=filter(None,slopes)
#remove non numeric values from the intercepts list
intercepts=filter(None,intercepts)
#calculate the over all intercept
over_all_intercept=float(sum(intercepts))/float(len(intercepts))
#calculate the over all slope
over_all_slope=float(sum(slopes))/float(len(slopes))


## for hard coded 90 periods, perform forecast from the last value from the predictions list

  new_pred=list()
n=90
new_value=last_pred
for i in xrange(1,n+1,1):
new_value=new_value+over_all_intercept+over_all_slope
new_pred.append(new_value)


## append the new_pred list to the predictions list

  predictions.append(new_pred)


## retrieve last months data from the existing series

start = int(time.time())-2592000


# set the end of the series 3 months

end = int(time.time()) + 5184000

forecastName = "holtWintersForecast(%s)" % series.name
forecastSeries = TimeSeries(forecastName, series.start, series.end
, series.step, predictions)
forecastSeries.pathExpression = forecastName


When I run though this it only, I only see future forecasting data for 14 days rather than 3 months.

Can somebody give some insight what might be going on here?