tl::dr How the time series data is set up (as two columns of data)

In the Forecasting function, time_series_data is a time series data set. It must be set up as can be seen in this example. The time must be labeled Period, and include a year and value. For example, 2015 Jan for monthly data, 2015 Q1 for quarterly data, or 2015 W1 for weekly data. The Value must be an integer, and Value must be a capital letter No other columns are needed.

How the time series needs to be set up to work with ForecastingEnsembles

The time_interval can be W (for weekly), M (for monthly) or Q (for quarterly)

Data may be imported to use for analysis.

The one chunk of code needed to automatically run the entire analysis

library(ForecastingEnsembles)

Forecasting(time_series_data = Oct_2024_all_nonfarm, train_amount = 0.60, number_of_intervals_to_forecast = 3, train_amount = 0.60, use_parallel = "Y", time_interval = "M")

When we run the function with this origianl data, the results in the Features table show the data is not stationary! The way this can be seen is in the Time Series Features table. It clearly shows Ndiffs = 1.0000, which means that we need to take 1 difference to make the data stationary.

Features shows the time series is NOT stationary, Ndiffs ≠0!

Note that the features are extremely important to conducting an accurate analysis. According to the book, Forecasting Principles and Practice, it is best to use stationary data. Note that “stationary data is data which does not depend on the time at which the series is observed.” (https://otexts.com/fpp3/stationarity.html#stationarity).

The importance of starting with stationary data is described in Forecasting Principles and Practice:

An important consideration when estimating a regression with ARMA errors is that all of the variables in the model must first be stationary. Thus, we first have to check that yt and all of the predictors (x1,t,…,xk,t) appear to be stationary. If we estimate the model when any of these are non-stationary, the estimated coefficients will not be consistent estimates (and therefore may not be meaningful).

source: https://otexts.com/fpp3/estimation.html

The list of features provided by the ForecastingEnsembles package can help determine if a time series is stationary, or if any steps are needed to make the series stationary. The most important feature to determine if a time series is stationary is the number of differences needed (if any) to make a time series stationary.More information on time series features may be found here:

https://otexts.com/fpp3/stlfeatures.html

https://otexts.com/fpp3/other-features.html

To make the time series stationary, we have a number of options. The easiest (and most common) is to difference the data. Here are three ways to convert time series data to be stationary:

If you need to difference data:

df <- df %>% mutate(Value = difference(Value)) %>% 
  slice(-1) # the slice(-1) removes the NA row

If you need to do seasonal differencing of data (in this example monthly data):

df %>% mutate(Value = difference(Value, differences = 12)) %>% 
  slice(13:nrow(df)) # the slice removes the first 12 NA rows

If you need to double difference data (do the difference twice):

df <- df %>% mutate(Value = difference(difference(Value)))  # Note the difference(difference(Value)) part of the equation

We only need to do one difference, and no seasonal differences, so this is very easy:

Oct_2024_all_nonfarm <- Oct_2024_all_nonfarm %>% mutate(Value = difference(Value))

Now our data is stationary, and the rest of the process is extremely easy to do.

We will be using the October 2024 all employees (differenced data) data in this example. The origianl data is not stationary, as we saw, and it was indicated that one difference was needed to make the data stationary. We will use the stationary data we achieved by differencing the data in this example. We are looking at the one month change in the number of all employees in our analysis.

If we use the time series for all employees, it can be seen that the number of differences is 0, which indicates the time series data is stationary. This can also be checked using the unitroot_kpss test, which also confirms the data is stationary. With the kpss test, a small p-value (less than 0.05) indicates that differencing is required. The p-value here is 0.100, which supports the decision that differencing is not required for this time series.

The list of features for the Oct_2024_all_employees data set is:

Features

Now we can run the Forecasting function, and ForecastingEnsembles takes care of everything for us!

library(ForecastingEnsembles)

Forecasting(time_series_data = Oct_2024_all_nonfarm, train_amount = 0.60, number_of_intervals_to_forecast = 3, train_amount = 0.60, use_parallel = "Y", time_interval = "M")

The function automatically returns the following:

Plots

The function returns the following plots (example used is Oct_2024_all_employees):

• Value per unit of time (the basic plot):

Value per unit of time

• Individual periods (it can be seen what happens each period.

Plot of individual periods for each year

• Value vs trend. This gives the actual value (in black) vs the trend (in red)

• Value vs seasonally adjusted value:

Value vs seasonally adjusted amount

• Full decomposition on one plot (Value, trend, season_year, remainder)

Full decomposition plots

• Anomalies (the blue dotted line is ± 1 standard deviation from 0, the red dotted line is ± 2 standard deviations from 0

Anomalies

ª Subseasons (can see each subseason independently):

Subseasons

• Multiple lags

Multiple lags

• Innovation residuals

Innovation residuals

• Autocorrelation function

Autocorrelation

Histogram of residuals

Histogram_of_residuals

• Actual vs predicted

Actual_vs_predicted

Actual vs residuals

Summary tables

• Head (top) of the time series

Head of the time series data

• Tail of the time series data

Tail of the time series data

• Time series features

Time series features

• Quartiles

Time series quartiles

• Forecast with the model with the lowest AICc score

Forecast with the model with the lowest AICc score

• Accuracy scores for all time series models

Accuracy for all models

• Min, mean, max, mean of 3 most recent

Min, mean, and max values

List of 23 time series models used by the package

Linear (4 models, individual, individual + season, individual + trend, individual + season + trend)

ARIMA (4 models, individual, individual + season, individual + trend, individual + season + trend)

Deterministic

Stochastic

ETS (4 models, individual, individual + season, individual + trend, individual + season + trend)

Holt-Winters (3 models, Additive, Multiplicative, Damped)

Fourier (6 models, K=1, K=2, K-3, K=4, K=5, K=6)

The 23 models are fit on the training data, and the accuracy is measured against the test data using AICc.

The excellent text Forecasting Principles and Practice cites the reason for using AICc when evaluating time series models:

Consequently, we recommend that one of the AICc, AIC, or CV statistics be used, each of which has forecasting as their objective. If the value of T is large enough, they will all lead to the same model. In most of the examples in this book, we use the AICc value to select the forecasting model.

Source: https://otexts.com/fpp3/selecting-predictors.html

The ForecastingEnsembles package will also use the lowest AICc value to select the optimal forecasting model.