Time series

Plotting one or several series

timeseries_plot() accepts a ts object, a numeric vector or a data frame with time, value and (optionally) group columns. Passing the long-form data frame with a grouping column draws both series at once, each in its own colour, and a moving-average overlay is one argument away.

timeseries_plot(monthly_sales, time = date, value = sales, group = series,
                rolling = 12, title = "Monthly sales by product line",
                y_lab = "Units")

Twelve months is an even window, so the overlay is the 2×12 moving average that the caption names (Hyndman & Athanasopoulos, 2021, Section 3.3). It is a twelve-month average followed by a two-month one, which centres it on each month.

For the single-series views (decomposition, autocorrelation, the seasonal plot and forecasting) we extract one line as a monthly ts object of frequency 12.

indoor <- subset(monthly_sales, series == "indoor")
indoor <- indoor[order(indoor$date), ]
indoor_ts <- ts(indoor$sales, start = c(2018, 1), frequency = 12)

Decomposition

decompose_plot() separates a seasonal series into trend, seasonal and remainder components. Use method = "stl" (the default, loess-based) or method = "classical". Setting confidence = TRUE shades a band around the smoothed trend, from the spread of the remainder, so the scale of the unexplained variation is visible rather than implied by the line alone.

decompose_plot(indoor_ts, confidence = TRUE, title = "Indoor sales, decomposed")

Classical decomposition holds the seasonal component fixed across the whole series, and so does STL (Cleveland et al., 1990) with its default s_window = "periodic".

decompose_plot(indoor_ts, method = "classical",
               title = "Indoor sales, classical decomposition")

A numeric s_window lets the STL seasonal component change from year to year. It is the number of consecutive years used to estimate each seasonal value, an odd number of at least 7, so a smaller window lets the pattern change faster. The bundled series has a fixed seasonal pattern by construction, so the effect shows better on AirPassengers, whose seasonal swing grows with the number of passengers.

decompose_plot(AirPassengers, s_window = 13,
               title = "Air passengers, with a 13-year seasonal window")

Autocorrelation

acf_plot() draws the autocorrelation (or, with type = "partial", the partial autocorrelation) function, with approximate significance bounds. The spikes at multiples of twelve are the annual seasonality.

acf_plot(indoor_ts)

acf_plot(indoor_ts, type = "partial")

The seasonal pattern up close

seasonal_plot() draws a seasonal-subseries (cycle) plot: one small panel per month, with the value traced across successive years and a reference line at each month’s mean. This shows the seasonal shape (differences between panels) and the year-on-year trend within each month (the slope inside each panel) at the same time, something a single overlaid line cannot do.

seasonal_plot(indoor_ts, title = "Indoor sales: monthly subseries")

With style = "season" every year becomes its own line over the months on a shared axis, which is handy for spotting an unusual year.

seasonal_plot(indoor_ts, style = "season",
              title = "Indoor sales: one line per year")

Forecasting

ts_forecast() forecasts by decomposition (Hyndman & Athanasopoulos, 2021, Section 5.7). It removes the seasonal component that STL estimates, forecasts what remains with a random walk with drift and adds the last year’s seasonal pattern back. Its prediction intervals are those of the random walk with drift, which widen with the horizon (Hyndman & Athanasopoulos, 2021, Section 5.5).

fc <- ts_forecast(indoor_ts, h = 18, level = 0.9)
head(fc)

      time      fit      lwr      upr
1 2024.000 316.3669 291.6190 341.1148
2 2024.083 334.7537 299.5126 369.9948
3 2024.167 346.3072 302.8512 389.7631
4 2024.250 359.1704 308.6539 409.6869
5 2024.333 351.7003 294.8458 408.5547
6 2024.417 346.0037 283.3144 408.6930

Passing an integer horizon straight to timeseries_plot() overlays that forecast on the history: the point forecast continues the line and the shaded ribbon shows the (growing) 90% prediction interval, named in the caption.

timeseries_plot(indoor_ts, forecast = 18, level = 0.9,
                title = "Indoor sales with an 18-month forecast",
                y_lab = "Units")

The model assumes a seasonal pattern that adds to the level and stays the same from year to year. Its band treats that pattern as known, which leaves out the uncertainty in estimating it. In a rolling-origin backtest on five classic series whose seasonal swing does not grow with their level, the nominal 95% band covered 92% of one-step-ahead outcomes. From three to 12 steps ahead, it covered 99%. The band therefore runs somewhat narrow at the shortest horizons and wide further out, where the uncertainty of a random walk keeps growing while these series stay close to their trend. When the swing does grow with the level, as it does for AirPassengers, set lambda = 0 to forecast the logarithm. The forecast comes back on the original scale, where the point forecast is the median of the forecast distribution (Hyndman & Athanasopoulos, 2021, Section 5.6).

timeseries_plot(AirPassengers, forecast = 24, level = 0.9, lambda = 0,
                title = "Air passengers with a 24-month forecast",
                y_lab = "Passengers")

For a different model, fit it yourself (for example with forecast::forecast()) and pass the resulting time/fit/lwr/upr columns to timeseries_plot(forecast = ) as a data frame.