You can see in the arima code that there is a seasonal component that is set to (0,0,0), it is the seasonal AR, I, and MA component that you can change the values for. So if you're using an AR(1) that also has a seasonal AR(12) (annual seasonal AR), then the seasonal c=(0,0,0) vector should be (1,0,0) and the period should be changed from NA as well to say what the period of the season is.
arima(x, order = c(0, 0, 0),
seasonal = list(order = c(0, 0, 0), period = NA),
xreg = NULL, include.mean = TRUE,
transform.pars = TRUE,
fixed = NULL, init = NULL,
method = c("CSS-ML", "ML", "CSS"),
n.cond, optim.method = "BFGS",
optim.control = list(), kappa = 1e6)
Modeling daily electricity demand is a data intensive effort. To simplify this, it's easier to start "zoomed out", estimating monthly loads. Here's an article (with a Youtube video) that describes a monthly model that is simple and easy to understand. The article includes R code:
http://revgr.com/2012/11/06/all-forecasts-are-wrong-but-some-generate-fewer-complaints/
As you "zoom in" to shorter time frames the problem gets more and more complicated. For example, the monthly model includes an integer 12 months/year and starts at the beginning of month 1, while a weekly model includes a non-integer 52.18 weeks/year and might begin at the start of a week, middle of the week, end of the week, etc (i.e. you can't directly compare "week 1" of one year to "week 1" of the next year, they start on different days). It gets more complicated when you drop down to daily or hourly time frames.
The hierarchy in time frames, starting with the longest time frame, is typically:
1) Population growth and economic activity.
2) Long term seasonal temperature terms (summer, winter, etc).
3) Day of the week (Tuesday, Wednesday and Thursday are typically similar workdays; the remaining days have their own individual "day-of-the-week" values).
4) Holidays, the day before and the day after a holiday (many holidays have a similar value as a typical Sunday "day-of-the-week" value).
5) Temperature due to time of day, cooler nights, warmer days, is the sun shining, is it raining, etc. (this is a refinement of item 2 above).
6) Work load during the day. People are typically at home during the night and at work during the day, so lot of electricity consuming workplaces shut down at night.
7) Other terms such as humidity, daylight savings time, etc.
The bottom line is, at the daily and hourly time frames, a lot of data (and complexity) is required.
You can Google "daily electrical load models" (or hourly models) and various papers will show up. Some are based on neural nets, support vector machines, etc. Here's a link to a paper by Rob Hyndman that explains another technique.
http://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm09771#.UrNTUtJDuyw
The methods used in that paper are in the "forecast" package:
http://robjhyndman.com/software/forecast/
Best Answer
A couple of things.
First, you are doing a good job by including multiple seasonalities. However:
Why do you include a seasonal cycle of length 182.5*24 for hourly data, i.e., half a year? Your seasonal cycles of length 24 already match daily cycles (day vs. night), and the ones of length 365*24 match yearly ones (summer vs. winter). I do not see a need for a cycle that repeats every six months.
However, there often is a difference between weekday and weekend electricity consumption, so it would be a good idea to include a cycle of length 7*24.
Next, don't misread the
stlplot. Note the grey rectangles on the right. The height is the same across all four panels in terms of y values. That is, what looks like a clear decreasing trend is a far weaker signal than the other components. Imagine rescaling the trend panel by squeezing it vertically until its grey rectangle is the same height as the grey rectangle in, say, the seasonal panel.Finally, I would typically recommend a
tbatsmodel to model electricity demand and/or load, which is exactly what you already did. If yourtbatsmodel is not satisfactory, you will need to go farther to the frontiers of electricity load forecasting. For instance, I recommend Hong & Fan (2016). "Probabilistic electric load forecasting: A tutorial review". International Journal of Forecasting, 32(3): 914-938. You could also search for other articles on "load forecasting" in the IJF or elsewhere.Finally, I took the liberty of adding the multiple-seasonalities tag to your question. Previous posts in this tag may be helpful.