# Introduction to Pattern Sequence based Forecasting (PSF) algorithm In PSF: Forecasting of Univariate Time Series Using the Pattern Sequence-Based Forecasting (PSF) Algorithm

## Introduction

The Algorithm Pattern Sequence based Forecasting (PSF) was first proposed by Martinez Alvarez, et al., 2008 and then modified and suggested improvement by Martinez Alvarez, et al., 2011. The technical detailes are mentioned in referenced articles. PSF algorithm consists of various statistical operations like:

• Data Normalization/ Denormalization
• Calculation of optimum Window size (W)
• Calculation of optimum cluster size (k)
• Pattern Sequence based Forecasting
• RMSE/MAE Calculation, etc..

## Example

This section discusses about the examples to introduce the use of the PSF package and to compare it with auto.arima() and ets() functions, which are well accepted functions in the R community working over time series forecasting techniques. The data used in this example are ’nottem’ and ’sunspots’ which are the standard time series dataset available in R. The ’nottem’ dataset is the average air temperatures at Nottingham Castle in degrees Fahrenheit, collected for 20 years, on monthly basis.

Similarly, ’sunspots’ dataset is mean relative sunspot numbers from 1749 to 1983, measured on monthly basis. First of all, the psf() function from PSF package is used to forecast the future values. For both datasets, all the recorded values except for the final year are considered as training data, and the last year is used for testing purposes. The predicted values for final year with psf() function for both datasets are now discussed.

#### Install library

```library(PSF)
```

#### Model building for ’nottem’ dataset with psf() function.

```nottem_model <- psf(nottem)
nottem_model
```

#### Model building for ’sunspots’ dataset with psf() function.

```sunspots_model <- psf(sunspots)
sunspots_model
```

#### Perform predictions from trained PSF model for ’nottem’ dataset using the standard predict() function.

```nottem_preds <- predict(nottem_model, n.ahead = 12)
nottem_preds
```

#### Perform predictions from trained PSF model for ’sunspots’ dataset using the standard predict() function.

```sunspots_preds <- predict(sunspots_model, n.ahead = 48)
sunspots_preds
```

To represent the prediction performance in plot format, the plot() function is used as shown in the following code.

#### Plot for 'nottem' dataset

```plot(nottem_model, nottem_preds)
```

#### Plot for 'sunspots' dataset

```plot(sunspots_model, sunspots_preds)
```

## Comparison of `psf()` with `auto.arima()` and `ets()` functions:

Example below shows the comparisons for `psf()`, `auto.arima()` and `ets()` functions when using the Root Mean Square Error (RMSE) parameter as metric, for ’sunspots’ dataset. In order to avail more accurate and robust comparison results, error values are calculated for 5 times and the mean value of error values for methods under comparison are also shown. These values clearly state that 'psf()' function is able to outperform the comparative time series prediction methods. Additionally, the reader might want to refer to the results published in the original work Martinez Alvarez et al. (2011), in which it was shown that PSF outperformed many different methods when applied to electricity prices and demand forecasting.

```library(PSF)
library(forecast)
options(warn=-1)

## Consider data `sunspots` with removal of last years's readings
# Training Data
train <- sunspots[1:2772]

# Test Data
test <- sunspots[2773:2820]

PSF <- NULL
ARIMA <- NULL
ETS <- NULL

for(i in 1:5)
{
set.seed(i)

# for PSF
psf_model <- psf(train)
a <- predict(psf_model, n.ahead = 48)

# for ARIMA
b <- forecast(auto.arima(train), 48)\$mean

# for ets
c <- as.numeric(forecast(ets(train), 48)\$mean)

## For Error Calculations
# Error for PSF
PSF[i] <- sqrt(mean((test - a)^2))
# Error for ARIMA
ARIMA[i] <- sqrt(mean((test - b)^2))
# Error for ETS
ETS[i] <- sqrt(mean((test - c)^2))

}

## Error values for PSF
PSF
mean(PSF)

## Error values for ARIMA
ARIMA
mean(ARIMA)

## Error values for ETS
ETS
mean(ETS)
```

## References

Martínez-Álvarez, F., Troncoso, A., Riquelme, J.C. and Ruiz, J.S.A., 2008, December. LBF: A labeled-based forecasting algorithm and its application to electricity price time series. In Data Mining, 2008. ICDM’08. Eighth IEEE International Conference on (pp. 453-461). IEEE.

Martinez Alvarez, F., Troncoso, A., Riquelme, J.C. and Aguilar Ruiz, J.S., 2011. Energy time series forecasting based on pattern sequence similarity. Knowledge and Data Engineering, IEEE Transactions on, 23(8), pp.1230-1243.

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PSF documentation built on May 2, 2019, 2:10 a.m.