Time series analysis – Meaning, Definitions, Nature, Scope, Importance, Objectives, Components, Models

In this article we will provide an overview of time series analysis, including its meaning, definitions, nature, scope, importance, objectives, components, and models.

Meaning of Time Series Analysis

Meaning of Time Series Analysis : Time series analysis is a statistical method used to analyze data that is collected over time, where the order of the observations is important. In other words, it involves analyzing and interpreting data that is sequentially ordered, such as stock prices, weather data, economic indicators, or other types of data that are recorded at regular intervals.

In order to evaluate the performance of a company, its past can be compared with the present data. When comparisons of past and present data are done, the process is known as Time Series Analysis. Time series are stretched over a period of time rather than being confined to a shorter time period. Time series analysis draws its important because it can help predict the future. Depending on the past and future trends, time series are able to predict the future.

Time series analysis is helpful in financial planning as it offers insight into the future data depending on the present and past data of performance. It can lead to the estimation of an expected time’s data by checking the current and past data. That means, time series is used to determine the future by using the trends and valuations of the past and present.

Definitions of Time Series Analysis

Definitions of Time Series Analysis : Time series analysis refers to the process of examining and analyzing the patterns, trends, and characteristics of a dataset that changes over time. It involves studying the past behavior of a variable in order to make predictions about its future behavior. Time series analysis often involves statistical techniques and modeling approaches to extract meaningful insights from time-dependent data.

some prominent statisticians and experts definitions in the field include:

1. “Time series analysis is the process of analyzing and modeling data collected sequentially over time in order to understand the underlying patterns, trends, and relationships, and make forecasts for the future.” – George E. P. Box and Gwilym M. Jenkins, renowned statisticians and authors of the classic book “Time Series Analysis: Forecasting and Control.”
2. “Time series analysis is the study of data collected over time to extract meaningful statistics, detect patterns and trends, and make predictions for the future, taking into account the inherent characteristics of time-varying data.” – Shumway and Stoffer, authors of the textbook “Time Series Analysis and Its Applications: With R Examples.”
3. “Time series analysis is the statistical analysis of data that is collected over time to uncover patterns, trends, and dependencies, and to make forecasts or estimate parameters of interest, using appropriate models and methods.” – Ruey S. Tsay, renowned statistician and author of the book “Analysis of Financial Time Series.”
4. “Time series analysis is a branch of statistics that deals with the analysis of data collected sequentially over time, with the goal of understanding the behavior of the data, identifying patterns and trends, and making forecasts for the future.” – Chatfield, author of the book “The Analysis of Time Series: An Introduction.”
5. “Time series analysis is the process of examining and modeling data collected over time to understand the underlying structure and behavior of the data, and to make informed decisions based on the insights obtained from the analysis.” – Brockwell and Davis, authors of the textbook “Introduction to Time Series and Forecasting.”

Meaning and Definitions of Time Series Analysis, Nature Scope of Time Series Analysis, Importance Objectives of Time Series Analysis, Components and Models.

Nature of Time Series Analysis

• The nature of time series data is dynamic, as it captures the changes and fluctuations in a variable over time.
• Time series data can exhibit various patterns, such as trend, seasonality, cyclicity, and irregularity.
• These patterns can provide valuable information for forecasting and decision-making.

Scope of Time Series Analysis

The scope of time series analysis is wide and diverse, as it is applied in various fields, including

• finance,
• economics,
• business,
• meteorology,
• medicine,
• social sciences, and
• many others.
• Time series analysis is used for forecasting future values,
• identifying underlying patterns and trends,
• detecting anomalies,
• understanding the impact of past events, and
• making informed decisions based on historical data.

Importance of Time Series Analysis

Importance: Time series analysis is important for several reasons:

1. Forecasting: It allows businesses and organizations to make informed predictions about future values of a variable, which can aid in planning, budgeting, and decision-making.
2. Pattern recognition: It helps in identifying patterns and trends in historical data, which can provide insights into the behavior of the variable over time and inform strategic decisions.
3. Anomaly detection: Time series analysis can detect anomalies or outliers in data, which can signal unusual events or behaviors that may require further investigation.
4. Monitoring and control: It enables real-time monitoring of data to identify changes or shifts in patterns, helping in quality control, process optimization, and performance tracking.\

Objectives of Time Series Analysis

Objectives: The main objectives of time series analysis are:

1. Understanding the historical behavior of a variable: Time series analysis helps in studying the patterns, trends, and characteristics of a variable over time to gain insights into its historical behavior.
2. Forecasting future values: It aims to make accurate predictions about future values of a variable based on its past behavior.
3. Identifying underlying patterns: Time series analysis helps in identifying underlying patterns, such as trend, seasonality, and cyclicity, that may exist in the data.
4. It enables us to study the past behavior of the phenomenon under consideration, i.e., to determine the type and nature of the variations in the data.
5. The segregation and study of the various components is of paramount importance to a businessman in the planning of future operations and in the formulation of executive and policy decisions.
6. It helps to compare the actual current performance or accomplishments with the expected ones (on the basis of past performances) and analyze the causes of such variations, if any.
7. It enables us to predict or estimate or forecast the behavior of the phenomenon in the future which is very essential for business planning.
8. It helps us to compare the changes in the values of different phenomena at different times or places, etc.

Meaning and Definitions of Time Series Analysis, Nature Scope of Time Series Analysis, Importance Objectives of Time Series Analysis, Components and Models.

Components of Time Series Analysis

The reasons or forces that change the attributes of a time series are known as the Components of Time Series.

The following are the components of time series −

• Trend
• Seasonal Variations
• Cyclical Variations
• Random or Irregular Movements

Trend

Trend shows a common tendency of data. It may move upward or increase or go downward or decrease over a certain, long period of time. The trend is a stable and long-term general tendency of movement of the data. To be a trend, it is not mandatory for the data to move in the same direction. The direction or movement may change over the long-term period but the overall tendency should remain the same in a trend.

Some of the examples of trends include – the number of schools, agricultural production, increase in population, etc. It is notable that the trend may move upward, go downward or remain stable over different sections of time.

A Trend can be either linear or non-linear.

Seasonal Variations

Seasonal variations are changes in time series that occur in the short term, usually within less than 12 months. They usually show the same pattern of upward or downward growth in the 12-month period of the time series. These variations are often recorded as hourly, daily, weekly, quarterly, and monthly schedules.

Seasonal variations occur due to natural or manmade forces or variations. The numerous seasons and manmade variations play a vital role in seasonal variations.

Example − The crops depend on the season, the sales of A.C,s going up during the summer and the use of umbrellas skyrocketing during the rainy season – all of these are seasonal variations.

Seasonal variations can be clearly seen in some cases of man-made conventions. The festivals, customs, fashions, habits, and various occasions, such as weddings impact the seasonal variations. An increase in business during the seasonal variation period should not be considered a better business condition.

Cyclical Variations

Variations in time series that occur themselves for the span of more than a year are called Cyclical Variations. Such oscillatory movements of time serious often have a duration of more than a year. One complete period of operation is called either a cycle or a ‘Business Cycle’.

Cyclic variations contain four phases – prosperity, recession, depression, and recovery. It may be regular or non-periodic in nature. Usually, cyclical variations occur due to a combination of two or more economic forces and their interactions.

Random or Irregular Movements

There is another kind of movement that can be seen in the case of time series. It is pure Irregular and Random Movement. As the name suggests, no hypothesis or trend can be used to suggest irregular or random movements in a time series. These outcomes are unforeseen, erratic, unpredictable, and uncontrollable in nature.

Earthquakes, war, famine, and floods are some examples of random time series components.

1. Time series data: This is the dataset that changes over time and is the primary input for time series analysis. It includes the historical values of the variable of interest, recorded at regular intervals, such as daily, monthly, or yearly.
2. Trend: Trend refers to the long-term movement or direction of a variable, which can be increasing, decreasing, or stable.
3. Seasonality: Seasonality refers to the repeating patterns or cycles that occur at fixed intervals within a time series data, such as daily, weekly, or yearly.
4. Cyclicity: Cyclicity refers to the non-regular patterns or cycles that occur in a time series data, which may not have a fixed interval.
5. Irregularity: Irregularity refers to the random or unpredictable fluctuations in a time series data that do not follow any specific pattern.

Meaning and Definitions of Time Series Analysis, Nature Scope of Time Series Analysis, Importance Objectives of Time Series Analysis, Components and Models.

Models of Time Series Analysis

Mathematical Models of Time Series Analysis

For analyzing time series, we usually have two models of time series analysis; (1) multiplicative model; and (2) additive model.

(1) Multiplicative model of Time Series Analysis :

The multiplicative model of time series Analysis assumes that the various components interact in a multiplicative manner to produce the given values of the overall time series and can be stated as under:

Y = T × C × S × I

where

Y = observed values of time series,

T = Trend,

C = Cyclical fluctuations,

S = Seasonal fluctuations / variations

I = Irregular fluctuations.

(2) Additive model of Time Series Analysis

Additive model considers the total of various components resulting in the given values of the overall time series and can be stated as:

Y = T + C + S + I

There are various methods of isolating trends from the given series viz., the free hand method, semi-average method, method of moving averages, method of least squares, and similarly there are methods of measuring cyclical and seasonal variations, and whatever variations are left over are considered as random or irregular fluctuations.

Implication and Limitation of Additive Model

• This implies that the trend, however, fast or slow, it may be, has no effect on the seasonal and cyclical components ; nor do seasonal swings have any impact on cyclical variations and conversely.
• However, this assumption is not true in most of the economic and business time series where the four components of the time series are not independent of each other.
• For instance, the seasonal or cyclical variations may virtually be wiped off by very sharp rising or declining trend.
• Similarly, strong and powerful seasonal swings may intensify or even precipitate a change in the cyclical fluctuations.

(3) Mixed Models of Time Series Analysis

In addition to the additive and multiplicative models discussed above, the components in a time series may be combined in a large number of other ways. The different models, defined under different assumptions, will yield different results. Some of the mixed models resulting from different combinations of additive and multiplicative models are given below :

Y = TCS + I

Y = TC + SI

Y = T + SCI

Y = T + S + CI

Importance Objectives of Time Series Analysis

Time Series Analysis Methods

Mock Tests and Test Series