Simple Moving Average is a method of time series smoothing and is actually a very basic forecasting technique. It does not need estimation of parameters, but rather is based on order selection. It is a part of smooth package.
Let’s load the necessary packages:
require(smooth)By default SMA does order selection based on AICc and returns the model with the lowest value:
y <- structure(c(2158.1, 1086.4, 1154.7, 1125.6, 920, 2188.6, 829.2,
1353.1, 947.2, 1816.8, 1624.5, 868.5, 1783.3, 1713.1, 3479.7,
2429.4, 3074.3, 3427.4, 2783.7, 1968.7, 2045.6, 1471.3, 2763.7,
2328.4, 1821, 2409.8, 3485.8, 3289.2, 3048.3, 2914.1, 2173.9,
3018.4, 2200.1, 6844.3, 4160.4, 1548.8, 3238.9, 3252.2, 3278.8,
1766.8, 3572.8, 3467.6, 7464.7, 2748.4, 5126.7, 2870.8, 2170.2,
4326.8, 3220.7, 3586, 3249.5, 3222.5, 2488.5, 3332.4, 2036.1,
1968.2, 2967.2, 3151.6, 1610.5, 3985, 3894.1, 4625.5, 3291.7,
3065.6, 2316.5, 2453.4, 4582.8, 2291.2, 3555.5, 1785, 2020, 2026.8,
2102.9, 2307.7, 6242.1, 6170.5, 1863.5, 6318.9, 3992.8, 3435.1,
1585.8, 2106.8, 1892.1, 4310.6, 6168, 7247.4, 3579.7, 6365.2,
4658.9, 6911.8, 2143.7, 5973.9, 4017.2, 4473, 3591.9, 4676.5,
8749.1, 11931.2, 8572.3, 8257.7, 11930.5, 15757.6, 5920.5, 3064.3,
5472, 8634.7, 5032, 6236, 6356, 9857.8, 6322.2, 7907, 13842.4,
13665.1, 3272), .Tsp = c(1983, 1992.5, 12), class = "ts")
sma(y, h=18, silent=FALSE)## Time elapsed: 0.09 seconds
## Model estimated: SMA(13)
## Initial values were produced using backcasting.
##
## Loss function type: MSE; Loss function value: 4393167.5848
## Error standard deviation: 2114.456
## Sample size: 115
## Number of estimated parameters: 2
## Number of degrees of freedom: 113
## Information criteria:
## AIC AICc BIC BICc
## 2089.345 2089.452 2094.835 2095.089
It appears that SMA(13) is the optimal model for this time series, which is not obvious. Note also that the forecast trajectory of SMA(13) is not just a straight line. This is because the actual values are used in construction of point forecasts up to h=13.