# Time Serie - Seasonality (Cycle detection)

### Table of Contents

## 1 - About

Seasonality is a cycle in time serie.

## 2 - Articles Related

## 3 - Methods

### 3.1 - Regression with Season as Dummy Variable

The season is used a discreet regression variable and code it as dummy variables).

For instance:

- 1 if it's the season
- 0 if it's not the season

If you have more than one type of season, then you may need various dummy variables.

### 3.2 - Seasonal Index

If you have five Decembers, then you should have five June. Having five of some month and six of other months will skew the seasonal indices.

Calculate a seasonal index for each month on past data.

If the average monthly sales is 100%, then the value in each month shows how that month compares to the average. Example:

- January can be 54.8% of the average month whereas December can 256.19% of the average month.

Do a normal regression and apply then this index to the forecast value.

### 3.3 - Holt-Winters method

The Holt-Winters method was designed to handle data where there is a conventional seasonal cycle across the course of a year, such as monthly seasonality. However, many series have multiple cycles: the demand for electricity will have hourly (patterns across the hours of a day), daily (patterns across the days of the week), and monthly cycles. Similar patterns occur in the number of calls received by call centers or the workload faced by hospitals.

### 3.4 - Fast Fourier Transform

FFT is a good tool to detect seasonality if we have a good amount of historical data. See http://nerds.airbnb.com/anomaly-detection

## 4 - Statistics

### 4.1 - R Squared

A R-Squared value of 0.0999 will means that straight-line forecasting is not going to yield an accurate forecast.