SimpleExpSmoothing.jl

Implementing Simple Exponential Smoothing (SES) in Julia.

Table of Contents

• Installation
• Basic Tour
• Customization

Installation

First, git clone and cd into the package directory.

Then, in Julia, do: ]activate . and instantiate

Basic Tour

using SimpleExpSmoothing

y = [445.36, 453.2, 454.41, 422.38, 456.04, 440.39, 425.19, 486.21, 500.43, 521.28, 
     508.95, 488.89, 509.87, 456.72, 473.82, 525.95, 549.83, 542.32] # Data to forecast on. Cite: [1]
mdl = ExponentialSmoothing(y) # Initialize SES model

fit!(mdl) # Fit the model. Find optimal parameters for SES.
yhat = predict(mdl) # Compute the forecast based on determined parameters

At this point, yhat will look something like this:

446.5735923427146
445.561818502492
451.9297824011145
453.9975437047159
427.6379479108166
451.31678329980605
442.2071069188588
428.01991818111446
. . .
544.3769207888416
542.6620626999179
542.6620626999179 
543.542.6620626999179
542.6620626999179
542.6620626999179

To visualize the forecast, do this:

plot_ts(y, yhat) # Plots y and yhat against time.

Alternatively, to save some space, do this:

plot_ts(mdl) # Takes the ExponentialSmoothing object, makes predictions, and plots them.

Both methods of plotting will yield something like this:

Customization

While the example above showed the ExponentialSmoothing object being used with only 1 parameter, it is possible to use more:

# Inputted values will be used if they are specified. Otherwise, they will be computed.
mdl = ExponentialSmoothing(observations, h = 3) 
mdl = ExponentialSmoothing(observations, alpha = 0.4)
mdl = ExponentialSmoothing(observations, alpha = 0.25, init_level = 500.0)
mdl = ExponentialSmoothing(observations, h = 15, alpha = 0.3, init_level = 750.0)

Key:
h: Number of time steps to forecast (h > 0, default: 5)
alpha: Smoothing parameter used in SES. (0 < alpha < 1, default: nothing)
init_level: initial level value. (default: nothing)

If alpha or init_level is nothing, an estimated optimal value will be computed using L-BGFS.

Example

y = rand(1.:100., 25)
mdl = ExponentialSmoothing(y, h = 3, init_level = 2) # Since alpha is not specified, it will be computed.

plot_ts(mdl)

The output of the code above may look like this:

References

[1] Hyndman, R.J., & Athanasopoulos, G. (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia. OTexts.com/fpp2. Accessed on 03/31/2021.