imputeTS (version 1.5)

na.ma: Missing Value Imputation by Weighted Moving Average

Description

Missing value replacement by weighted moving average. Uses semi-adaptive window size to ensure all NAs are replaced.

Usage

na.ma(x, k = 4, weighting = "exponential")

Arguments

x

Numeric Vector (vector) or Time Series (ts) object in which missing values shall be replaced

k

integer width of the moving average window. Expands to both sides of the center element e.g. k=2 means 4 observations (2 left, 2 right) are taken into account. If all observations in the current window are NA, the window size is automatically increased

weighting

Weighting to be used. Accepts the following input:

• "simple" - Simple Moving Average (SMA)

"linear" - Linear Weighted Moving Average (LWMA) "exponential" - Exponential Weighted Moving Average (EWMA)

Value

• Vector (vector) or Time Series (ts) object (dependent on given input at parameter x)

Details

In this function missing values get replaced by moving average values. Moving Averages are also sometimes refered to as "moving mean", "rolling mean", "rolling average" or "running average". The mean in this implementation taken from an equal number of observations on either side of a central value. This means for an NA value at position i of a time series, the obervations i-1,i+1 and i+1, i+2 (assuming a window size of k=2) are used to calculate the mean. Since it can in case of long NA gaps also occur, that all values next to the central value are also NA, the algorithm has a semi-adaptive window size. Whenever there are less than 2 non-NA values in the complete window available, the window size is incrementally increased, till at least 2 non-NA values are there. In all other cases the algortihm sticks preset window size. Ther are options for using Simple Moving Average (SMA), Linear Weighted Moving Average (LWMA) and Exponential Weighted Moving Average (EWMA). SMA: all observations in the window are equally weighted for calculating the mean. LWMA: weights decrease in arithmetical progression. The observations directly next to a central value i, have weight 1/2, the observations one further away (i-2,i+2) have weight 1/3, the next (i-3,i+3) have weight 1/4, ... EWMA: uses weighting factors which decrease exponentially. The observations directly next to a central value i, have weight 1/2^1, the observations one further away (i-2,i+2) have weight 1/2^2, the next (i-3,i+3) have weight 1/2^3, ...

See Also

na.interpolation, na.kalman, na.locf, na.mean, na.random, na.replace, na.seadec, na.seasplit

Examples

#Prerequisite: Load Time series with missing values
x <- tsAirgap

#Example 1: Perform imputation with simple moving average
na.ma(x, weighting = "simple")

#Example 2: Perform imputation with exponential weighted moving average
na.ma(x)

#Example 3: Perform imputation with exponential weighted moving average, window size 6
na.ma(x, k=6)