Why ARIMA produces stable forecast results?

Question

I am new in R language. I have a time series data in seconds (15 second interval) for the period of 72 hours as shown below. I am using auto.arima() function for forecasting next 30 points in time series. The result produced by auto.arima() function is very bad in terms of forecasting values as shown below after the code. I request you to provide your suggestion on what action I need to take in arima implementation for making batter forecast.

timestamp ----------- value

1998-05-31 22:00:15 33

1998-05-31 22:00:30 36

1998-05-31 22:00:45 45

1998-05-31 22:01:00 36

1998-05-31 22:01:15 34

1998-05-31 22:01:30 47

1998-05-31 22:01:45 45 .................. .. .................. ..

I created xts time series and did forecast using auto.arima() function in R

wdata <- read.csv("D:/rwl/seconds/reqseconds1.csv", stringsAsFactors = FALSE)

wdata$Time <- as.POSIXct(wdata$Time, format="%d/%m/%Y %H:%M:%S")

wdata_xts <- xts(x=wdata$Request, order.by=wdata$Time, frequency = 60)

fitarima<-auto.arima(wdata_xts, ic="bic", test="kpss", trace = TRUE)

workloadforecast <- forecast(fitarima, h=12)

auto.arima () function produces stable forecast results as following

  Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95

43201 61.90968 50.00501 73.81435 43.70305 80.11631

43216 61.84863 49.77316 73.92409 43.38080 80.31646

43231 61.80162 49.61284 73.99041 43.16048 80.44276

43246 61.76543 49.49914 74.03172 43.00575 80.52511

43261 61.73756 49.41654 74.05859 42.89418 80.58095

43276 61.71611 49.35511 74.07711 42.81160 80.62062

43291 61.69959 49.30838 74.09080 42.74887 80.65031

43306 61.68687 49.27202 74.10173 42.69999 80.67375

43321 61.67708 49.24308 74.11108 42.66092 80.69324

43336 61.66954 49.21954 74.11954 42.62891 80.71018

43351 61.66374 49.19995 74.12752 42.60203 80.72545

43366 61.65927 49.18330 74.13523 42.57893 80.73961

All forecasted values are similar (around 61). Please provide your suggestions for improving forecasted results.

Answer 1

After reviewing your 259,200 record detailing 60 readings per minute for 60 minutes for 72 days .. I suggest that you create two predictor variables for an ARMAX model. The first predictor will be hourly totals. Create a series that has 4,320 hourly values and develop a prediction for the next 24 hours . Use this series and it's future values in the ARMAX model. Now create a series that has daily totals .. thus 72 historical values and a 1 period out forecast. Now construct an ARMA model using these two predictors and detect pulses, level shifts , local time trends and an arma structure.

Proceed to estimate this hybrid model and iterate until all coefficients are significant and the error process is white noise. This is the approach i would use with AUTOBOX or any other iterative self-checking time series package.