Time Series Forecasting — A Complete Guide (2023)

In this article I will explain the basics of time series forecasting and show how we can implement different forecasting models in Python.

Forecast is a word we usually associate with weather. As we listen to or watch the NEWS, there is always a separate segment called "Weather Report" where the NEWS commentator provides us with the weather forecast information. Why are forecasts so important? Well, simply because we can doinformed decisions.

Now, there are two main types of forecasting methods, namely qualitative forecasting and quantitative forecasting.

In qualitative forecasting, forecasting decisions depend on expert opinions. No data is available to examine the patterns to make forecasting decisions. Since human decisions are involved, there is a possibility of bias.

In quantitative forecasting, data with patterns are available and computers can capture these patterns well. Therefore, human decision-making is not involved, so there is no possibility of human bias.

If we assign a time or time component to the forecast, it willtime series predictionand the data is called astime series data.Statistically, time series forecasting is the process of analyzing the time series data using statistics and models to make predictions and make informed strategic decisions. It falls under quantitative forecasting.

Examples oftime series predictionare weather forecasts for the next week, predicting the closing price of a stock for each day, etc.

To make near-accurate forecasts, we need to collect the time series data over a period of time, analyze the data, and then create a model to help us make the forecast. But for this process, certain rules must be followed, which will help us to get almost accurate results.

Granularity Rule:This rule states that the more aggregated your forecasts are, the more accurate your predictions will be. This is because aggregated data has less variance and therefore less noise.

Frequency rule:We frequently need to update the data to capture new information that becomes available, which makes our forecasts more accurate.

Horizon rule:Avoid making predictions too far into the future. That is, we should make predictions over a short period of time and not too far into the future. This will provide more accurate forecasts.

Components of time series data

Let's understand the meaning of each component one by one.

1. Level: Every time series has a baseline. To this baseline we add various components to form a complete time series. This baseline is known asLevel.
2. Trend: Defines whether the time series increases or decreases over a period of time. That is, it has an uptrend (increasing) or a downtrend (decreasing). For eg. The above time series has an increasingTrend.
3. seasonality :It defines a pattern that repeats itself over a period of time. This pattern that repeats itselfregularlymeans asseasonality. In the chart above we can clearly see the seasonality component present.
4. cyclicality: Cyclicity is also a pattern in the time series data, but it repeats itselfaperiodic, which means it doesn't repeat at fixed intervals.
5. Noise: After we extract level, trend, seasonality/cyclicality, what is leftNoise. Noise is a completely random fluctuation in the data.

We get the above components if we decompose the time series. There are mainly two types of time series decomposition vizadditive seasonal decompositionandmultiplicative seasonal decomposition.

This is easy to understand: If the individual components of the present time series are added together to obtain the original time series, this is referred to as additive seasonal decomposition. If the individual components have to be multiplied in order to obtain the time series data, this is called multiplicative seasonal decomposition. The main reason for using one decomposition type over the other is that the residue should not show a pattern. That means it should just be random fluctuation.

Time Series Forecasting Python implementation

Using an example, we will now see how different forecasting techniques are implemented in Python and how effective they are.

First, let's understand the importance of the evaluation metrics that we will use to evaluate these forecasting techniques.

RMSE: RootMeanStormentedError is the square root of the mean square error (MSE). MSE is nothing more than a representation of how predicted values ​​differ from actual or true. We take the square root to avoid the negative sign, since errors can be positive or negative. It is represented by the following formula:

CARTE: MeanAabsolutePpercentEError is the measure of how accurate a forecasting system is. It measures this accuracy as a percentage and can be calculated as the average absolute percentage error for each period minus actual values ​​divided by actual values. It is represented by the following formula:

From whereIndeedis the true value andYpredictedis the predicted value at that particular point in time.nis the number of observations.

Both RMSE and MAPE should be as low as possible.

So here is the problem: Global Mart is an online super giant that operates worldwide. It takes orders and ships worldwide, serving 7 different geographic market segments – (Africa, APAC (Asia Pacific), Canada, EU (European Union), EMEA (Middle East), LATAM (Latin America), USA (United States). ) ). It covers all major product categories – consumer, business and home office. We mustforecast sales for the consistently most profitable market segment.

note: The code and graphics used in the article are present in the Python file whose link is given at the bottom of the article.

1. Import the required libraries
2. Read and understand the data
3. Exploratory data analysis
4. Data Preparation
5. Time Series Decomposition
6. Create and evaluate time series forecast

1. Import the required libraries

2.Read and understand the data

Our data has 51290 rows and 5 columns and there are no missing values.

3.Exploratory data analysis

We run the outlier analysis of various attributes and find that there are indeed outliers in the profit and revenue columns.

In the time series data there are observations at all timestamps and therefore we cannot delete the outliers as this leads to data loss and affects their continuity.

We ran univariate, bivariate and multivariate analysis and here are the graphs.

From the graphs above we can see thatCanada consumer is the most profitable market segmentandAPAC-Home Office is the leading market segment combination in terms of revenue.

According to the problem statement, we need to find 21 market segments by combining the respective 7 geographic markets for each of the 3 product segments. We create a columnmarket segmentby combining 2 columns, market and segment.

Train-Test-Split :We split the data so that the train set contains 42 months and the test set contains 6 months of data.

Persistently profitable market segment:The coefficient of variation is the ratio of the standard deviation to the mean. We need to find the market segment for which the value of the coefficient of variation brings the least profit. This is because a lower standard deviation means a lower earnings variability, which means earnings numbers for that region are more consistent over the given time period. We calculate the coefficient of variation for each of the 21 market segments for 42 months (train data) to decide which market segment is consistently profitable.

We think, thatAPAC consumersis the market segment with the lowest coefficient of variation. This means that the winning numbers for the APAC consumer market segment have been consistent over the period of the train set. Therefore, we choose this market segment to further calculate and predict sales values.

We filter the dataAPAC consumersMarket Segment and group the resulting data frame by order date to get the time series data that includes order date and sales. We call it data1.

Our time series data looks like this:

We perform the additive and multiplicative seasonal decomposition as follows:

The data clearly contain seasonal components. We build different time series forecasting models and compare themRMSE(Root Mean Squared Error) undMAP(Mean Absolute Percentage Error) values ​​for all models. Lower values ​​of RMSE and MAPE are desirable to conclude that a model is performing better. Accuracy is calculated as (100 — MAPE). The lower the MAPE value, the higher the accuracy.

We will now see different forecasting methods to forecast sales values.

Simple time series forecasting methods

3 methods that fall under it are the naive method, the simple average method and the simple moving average method.

The naive method simply transfers the last observation. The simple average uses the average of all observations for forecasting and the simple moving average method uses moving averages for forecasting.

The RMSE and MAPE values ​​are as follows:

As we can see from the figures above, among the simple forecasting methods, the simple moving average method performs best.

Exponential smoothing techniques

Namely, they are the Simple Exponential Smoothing technique, the Holt method with trend, and the Holt-Winter method.

While the simple averaging method gives equal weight to past observations, simple exponential smoothing gives more weight to recent observations than past ones. It captures the level in the data but does not capture trends or seasonality. The Holt method, on the other hand, can capture level and trend, but not seasonality. Holt Winter's method can capture all levels, trends and seasonalities.

We conclude that Holt Winters' additive method in the smoothing techniques is able to predict sales closer to actual values. The RMSE and MAPE values ​​for this method are lower than other model methods. This method is very good at capturing the trend and seasonality in the data.

Auto-Regressive Methods

Autoregressive methods use the regression technique to predict future observations using a linear combination of past observations. But for that the time series should follow 2 assumptions: stationarity and autocorrelation.

For a time series to be stationary, the mean, variance, and covariance should be constant. Autocorrelation helps us know how a variable is affected by its own lagged values.

There are 2 tests to confirm stationarity, as follows:

Kwiatkowski-Phillips-Schmidt-Shin (KPSS)-Test:

1. Null hypothesis (H 0 ): The series is stationary: p−value>0.05

2. Alternative hypothesis (H a ): The series is not stationary: p−value ≤ 0.05

Extended Dickey-Fuller (ADF) test:

1. Null hypothesis (H0 ): The series is not stationary : p−value>0.05

2. Alternative hypothesis (Ha): The series is stationary: p−value ≤ 0.05

We perform these tests on our time series data and conclude that the time series is not stationary. To make it stationary, we have to performdifferentiate(make mean constant) andTransformation(make variance constant).

We perform a train-test split and continue with the autoregressive techniques for prediction.

Automatic regression method (AR)

This method uses linear regression to predict the future observation using one or more past observations.

Moving Average (MA) Method

Here, future values ​​are forecast using past forecast errors in a regression-like model.

Automatic Regression Moving Average (ARMA) Method

It is a combination of AR and MA models.

Automatic Regressive Integrated Moving Average (ARIMA)

It is the same as the ARMA model, only has an additional integrated differentiation component. Previously, we applied both the Box-Cox transform and differentiation to the data to make the time series data stationary. Here we simply apply Box-Cox before building the model and let the model differentiate, i.e. H. the trend component itself.

Seasonal Auto-Regressive Integrated Moving Average (SARIMA)

SARIMA is the same as ARIMA, it just has an additional seasonal component.

After we have implemented all forecasting models, we calculate the RMSE and MAPE for all methods.

We conclude thatHolt Winters' additive methodandSeasonal Autoregressive Integrated Moving Average (SARIMA) technique.are the best for predicting sales for the data. Both methods have lower RMSE and MAPE values ​​and are able to capture the trend and seasonality components in the data well.

This completes our analysis. I hope the article was informative and easy to understand. Also, I hope you enjoyed analyzing the colorful graphics included in the analysis.

Feel free to comment and give your feedback.

You can connect with me on LinkedIn:https://www.linkedin.com/in/pathakpuja/

Please visit my GitHub profile for the Python codes. The code mentioned in the article as well as the graphics can be found here:https://github.com/pujappathak/Retail Giant Sales Forecast

References:

https://www.statisticshowto.com/probability-and-statistics/regression-analysis/rmse-root-mean-square-error/

https://www.statisticshowto.com/mean-absolute-percentage-error-mape/