# Easy Rolling Means with MazamaRollUtils

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Our goal in creating a new package of C++ rolling functions is to build up a suite of functions useful in environmental time series analysis. We want these functions to be available in a neutral environment with no underlying data model. The functions are as straightforward to use as is reasonably possible with a target audience of data analysts at any level of R expertise.

## Background

Analysis of time series data often involves applying “rolling” functions to calculate, *e.g.* a “moving average”. These functions are straightforward to write in any language and it makes sense to have C++ versions of common rolling functions available to R as they dramatically speed up calculations. Several packages exist that provide some version of this functionality:

- zoo – core R package with a specific data model
- seismicRoll – rolling functions focused on seismology
- RcppRoll – rolling functions for basic statistics

The initial release of **MazmaRollUtils** provides all the basic rolling functions with features like alignment and missing value removal along with additional capabilities for smoothing, damping and outlier detection — all common activities in time series analysis.

## Features

### Predictable Names

Many of the rolling functions in **MazamaRollUtils** have the names of familiar **R** functions with `roll_`

prepended. These functions calculate rolling versions of the expected statistic:

`roll_max()`

`roll_mean()`

`roll_median()`

`roll_min()`

`roll_prod()`

`roll_sd()`

`roll_sum()`

`roll_var()`

Additional rolling functions with no equivalent in base R include:

`roll_MAD()`

– Median Absolute Deviation`roll_hampel()`

– Hampel filter

Other functions wrap the rolling functions to provide enhanced functionality. These are not required to return vectors of the same length as the input data.

`findOutliers()`

– returns indices of outlier values identified by`roll_hampel()`

.

### Common Arguments

All of the `roll_~()`

functions accept the same arguments where appropriate:

`x`

– Numeric vector input.`width`

– Integer width of the rolling window.`by`

– Integer shift to use when sliding the window to the next location`align`

— Character position of the return value within the window. One of: “left”, “center” or “right”.`na.rm`

– Logical specifying whether values should be removed before the calculations within each window.

The `roll_mean()`

function also accepts:

`weights`

– Numeric vector of size`width`

specifying each window index weight. If`NULL`

, unit weights are used.

### Predictable Return Length

The output of each `roll_~()`

function is guaranteed to have the same length as the input vector, with varying stretches of `NA`

at one or both ends depending on arguments `width`

, `align`

and `na.rm`

. This makes it easy to align the return values with the input data.

## Examples

The example dataset included in the package contains a tiny amount of data but suffices to demonstrate usage of package functions.

### Basic Rolling Means

library(MazamaRollUtils) # Extract vectors from our example dataset t <- example_pm25$datetime x <- example_pm25$pm25 # Plot with 3- and 24-hr rolling means layout(matrix(seq(2))) plot(t, x, pch = 16, cex = 0.5) lines(t, roll_mean(x, width = 3), col = 'red') title("3-hour Rolling Mean") plot(t, x, pch = 16, cex = 0.5) lines(t, roll_mean(x, width = 24), col = 'red') title("24-hour Rolling Mean") layout(1)

### Using ‘width’, ‘align’, ‘by’ and ‘na.rm’

The next example uses all of the standard arguments to quickly calculate a daily maximum value and spread it out across all indices.

library(MazamaRollUtils) # Extract vectors from our example dataset t <- example_pm25$datetime x <- example_pm25$pm25 # Calculate the left-aligned 24-hr max every hour, ignoring NA values max_24hr <- roll_max(x, width = 24, align = "left", by = 1, na.rm = TRUE) # Calculate the left-aligned daily max once every 24 hours, ignoring NA values max_daily_day <- roll_max(x, width = 24, align = "left", by = 24, na.rm = TRUE) # Spread the max_daily_day value out to every hour with a right-aligned look "back" max_daily_hour <- roll_max(max_daily_day, width = 24, align = "right", by = 1, na.rm = TRUE) # Plot with 3- and 24-hr rolling means layout(matrix(seq(3))) plot(t, max_24hr, col = 'red') points(t, x, pch = 16, cex = 0.5) title("Rolling 24-hr Max") plot(t, max_daily_day, col = 'red') points(t, x, pch = 16, cex = 0.5) title("Daily 24-hr Max") plot(t, max_daily_hour, col = 'red') points(t, x, pch = 16, cex = 0.5) title("Hourly Daily Max") layout(1)

### Using roll_mean() with ‘weights’

The `roll_mean()`

function accepts a `weights`

argument that can be used to create a *weighted moving average*. The next example demonstrates creation of an exponential weighting function to be applied to our data.

library(MazamaRollUtils) # Extract vectors from our example dataset t <- example_pm25$datetime x <- example_pm25$pm25 # Create weights for a 9-element exponentially weighted window # See: https://en.wikipedia.org/wiki/Moving_average N <- 9 alpha <- 2/(N + 1) w <- (1-alpha)^(0:(N-1)) weights <- rev(w) # right aligned window EMA <- roll_mean(x, width = N, align = "right", weights = weights) # Plot Exponential Moving Average (EMA) plot(t, x, pch = 16, cex = 0.5) lines(t, EMA, col = 'red') title("9-Element Exponential Moving Average") layout(1)

*Best wishes for speedy time series analysis!*

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