Time Series Analysis: Definition, Components and Model

Time series data is commonly found when keeping an eye on industrial processes or tracking a company’s performance numbers. It is highly dependent on the quality and quantity of the data. In this blog, we will learn what time series analysis actually is, how it works, the components, and the model that is included.   

Table of Contents

• What is Time Series Analysis?
• Why Do We Need Time-Series Analysis?
• Components of Time Series Analysis
• When Not to Use Time Series Analysis?
• What is Stationarity in Time Series Analysis?
• ARIMA Model in Time Series Analysis
• Conclusion

What is Time Series Analysis?

In Python, time series analysis is used in studying and performing operations on data that is recorded over time at intervals such as quarterly, yearly, decade, century and so on. Time series analysis is also defined as the analysis and interpretation of data or events over time such as past, present, and future forecasting after detecting any hidden patterns and insights in the past data. Fields like finance, economics, meteorology, among many others, have popular use of time series analysis.

Built-in libraries and tools for time series analysis

In the Python programming language, we have dedicated built-in libraries and tools for time series analysis. Some of them are described below:

1. Pandas

It is a powerful, open-source, and simple library that is used for data manipulation and makes data cleansing easy and effective. It has series (single-dimensional) and data frames (multidimensional, made up of series). The name “Pandas” is derived from the word “Panel Data” which is multidimensional data that involves measurements over time. Pandas has many different functions and methods for working with time series data, which include, rolling window calculations, resampling, date-time indexing, etc. 

2. Numpy

Numpy stands for “Numerical Python” and is the most widely used library for linear algebra. It is used for performing mathematical and logical operations on multidimensional arrays. Numpy consists of various sets of functions that can be used for performing mathematical and logical operations

3. Matplotlib

Matplotlib is an open-source Python library that is used for data visualization. It created 2D graphs and plotted them using Python scripts. Once the plot is created, you can produce the output in a variety of hard copy formats, like PNG or GIF. It also provides an object-oriented API. 

4. Prophet

Prophet is an open-source forecasting tool developed by Facebook. It is designed for forecasting time series data that exhibits seasonality and trends. It is relatively easy to use and provides robust forecasting capabilities.

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Process To Follow Time Series Analysis

The steps for performing Time Series Analysis are:

• Data Preprocessing: It is the process of removing dirty, incomplete, noisy, and inconsistent data from the dataset so that it can give accurate outputs.
• Exploratory Data Analysis: Visualizing data through Exploratory Data Analysis (EDA) is a powerful tool for detecting any potential outliers and patterns, including seasonality.
• Modeling: On the basis of appropriate characteristics of time series data, it makes models like ARIMA and SARIMA.
• Training and Evaluation: Here the data set is split into test and training data sets, and performance evaluation is done with the help of metrics like Mean Absolute Error (MAE), Mean Squared Error (MSE), or Root Mean Squared Error (RMSE).
• Forecasting: This is the last step, and in this particular step we use our trained datasets to predict the outputs and visualize the results. 

Why Do We Need Time-Series Analysis? 

In time series analysis, we only have one variable. Assume you have a shoe-selling business, and you desire to know how many foot-wears you sold over the past six months. In this process, you would calculate all the sales of footwear during the last six months by summation. Suppose you have initiated the sales in the month of January and now what you are going to do is that you will keep a record of all the months separately and then you are going to add them up together and then you are going to get the desired output. But suppose you want to know the sales for the next three or six months? 

Now, you just have one variable in your head, that is, sales and now you need to forecast that according to another variable, that is time. In such cases when you have a single variable to predict in terms of another one, here comes TIME SERIES ANALYSIS. You can analyze what happened in the past to predict what may happen later.

Components Of Time Series Analysis

There are four different components of time series analysis, which are as follows:

• Trend
• Seasonality
• Irregularity
• Cyclic

Trend

A trend is nothing but a movement to relatively higher or lower values over a long period of time. When time series analysis shows a general pattern that is upward, we call it an Up-Trend and when it exhibits a lower pattern, we call it a Down-Trend. Whenever there is no trend or a straight line, we call it a horizontal trend.

For example: A new residential site is being built, and people are moving there. You opened a hardware shop over there and now at the beginning, everyone will buy hardware. So, the sales of the shop are high or we can say the trend is high. But after some time, when everyone has their own hardware, and every house is occupied, the trend may go down. Let’s say that the sales are up for the first two years, and then they go down.

Seasonality

It’s a repeating pattern within a fixed time period. For example, Diwali is celebrated all over India in the months of either October or November. Now, the sales of crackers in these months are very high as compared to other months of the year. This has been noticed for the past two years, five years, ten years, and so on, so it’s a repeating pattern within a fixed time period, while in trend this is not the case. Taking one more example of ice cream, the sales of ice cream go comparatively higher in summers than in winters, so this is a seasonality again. 

Irregularity

This is also known as noise or irrelevant data. It is inconsistent in nature, or, we can say, unsymmetric. Irregularity typically occurs for a brief period and does not repeat. For example, COVID-19 emerged suddenly within a decade. During the COVID pandemic, sales of sanitizers and masks were high, but after some time, these products have become less common. So, this is all happening erratically. You don’t know how many sales will occur, so this represents random variation, which is known as an irregularity. 

Cyclic

It is repeating up and down movements, so this means we can go over more than a year. Cyclic does not have any fixed patterns. They can happen anytime, like in a year in a decade, or maybe within six months. They keep on repeating and as a result, they are much harder to predict. 

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When not to Use Time Series Analysis?

Time series analysis may not be suitable in certain situations:

1. No time component

If the data does not have a clear time component, then time analysis is not required. Time series analysis is specifically meant for data where observations are recorded at different time intervals, say daily, monthly, or annually.

2. Insufficient data

Time series analysis often needs sufficient data points to identify patterns and trends. If you have little historical data, it will be difficult to perform effective time series analysis.

3. Non-stationary data:

Whenever we use Time Series Analysis, it is mandatory that some statistical metrics like mean and variation should be constant. If your data is not stable, you need to use variable or variables to make it suitable for analysis. In some cases, non-stationary data may require other methods. 

What is Stationarity in Time Series Analysis?

It is an important concept in the analysis of time. In the context of time series data, stationarity refers to the statistical properties of the rest of the data series where statistical properties (such as mean, variation, and autocorrelation) are present. Simply put, stationary time refers to a time series whose properties do not change over time.

Stationarity is an assumption in many time analysis methods and models because it makes it easier to analyze and thus allows for more accurate interpretation and prediction. When the time series is not stationary, then it becomes really hard to draw any conclusion or make predictions from the data

There are three important factors to consider when evaluating the position of a time series

1. The mean: The value remains constant over time. This means that the series should not exhibit any upward or downward trend.
2. Persistent variables: Variables at fixed intervals should remain constant overtime. This means that the spread or weakness of the product should not change over time.
3. Constant autocorrelation: The autocorrelation function measures the relationship between data points at different lags and previous data points over time. In a stable environment, the strength and nature of this relationship should not change over time.

If the term happens to be non-stationary, then you will need to difference the variable and make it stationary in order to use the time model, such as ARIMA or SARIMA. First, the models are used for stationary time series data, which can also produce useful predictions and analysis when applied.

Tests to check stationarity

Rolling Statistics

Instead of calculating a statistic for the entire data set, we calculate statistics for a subset, or window, of that data, adjusting the window for each new data encountered.

Augmented Dickey Fuller (ADF) Test

The null hypothesis is that the TS is non-stationary. The test results comprised Test Statistics and some critical values. 

ARIMA Model In Time Series Analysis

In Time Series Analysis, ARIMA stands for Auto-Regressive Integrated Moving Average. It is used to predict the future values of time series using historical data. 

Auto-Regressive Model

Wherever there is a correlation between historical and current data, the auto-regressive model came into the picture. The formula to calculate auto-regression is given below: 

It is a modified version of the slope formula with the target value being expressed as the sum of the intercept, the product of a coefficient, and the previous output, and an error correction term.

Integration

It is the difference between the current analysis and the previous analysis. It is used as a stationary time series. All values ​​are parameters of our ARIMA model. Instead of using different operators and models to represent ARIMA models, you use indicators to represent them. The parameters are:

• p: Previous market value for each period. It is derived from the autoregressive model.

• q: pre-delayed value of the error. It is obtained from moving averages.

• d: Number of times the data is changed to keep it constant. How many times the integration was done

Moving Average

A moving average is a statistical method that uses an updated average to help reduce noise. It uses the average price of a specific time. You can achieve this by taking different pieces of data and finding their average.

First, you consider a group of data points and average them. You can find the next average by subtracting the first value from the data and including the next value in the series.

Conclusion

In this Python tutorial on time series analysis first introduces time series and time series analysis. Next learn different components of time analysis, and the ARIMA model, which is a measurement model in time. Finally, you learn how to use time analysis in Python. We hope this helped you understand how to use time analysis in Python. To learn more about machine learning, check out Intellipaat’s Data Scientist course.