## What is Forecasting?

Forecasting is a methodology that uses historical data as inputs to make well-informed predictions about the course of future trends. Forecasting is the method of making forecasts based on historical and current data, most commonly by trend analysis. In the business world, forecasting is a basic statistical task. Forecasting is used by businesses to decide how to allocate their budgets or prepare for expected expenditures in the future. Forecasts help managers formulate and execute production plans by providing forecasts. The primary goal of forecasting is to make accurate predictions.

No one can predict future revenue, breakages, new equipment requirements, or investment returns because no one can see the future. However, in order to move the company forward, certain decisions must be taken and implemented. Many conditions necessitate forecasting: determining whether to construct another power plant in the next five years requires forecasts of potential demand; staffing a call centre next week requires forecasts of call volumes; forecasting stock requirements is needed when stocking an inventory.

On March 11, 2020, the World Health Organization (WHO) declared the novel coronavirus (Covid19) outbreak a global pandemic. The time series model selected to make the prediction is called Auto-Regressive Integrated Moving Average (ARIMA) model.

Forecasting should be an important part of management's decision-making processes since it can directly affect many areas of a company. Depending on the application, modern organizations require short-, medium-, and long-term forecasts.

### Short Term Forecasts

Short-term predictions are typically made for tactical purposes such as production planning and control, short-term cash needs, and seasonal revenue fluctuations changes. Personnel, manufacturing, and transportation scheduling all require short-term forecasts. Demand forecasts are often needed as part of the scheduling process. These forecasts are for less than one year, with a typical duration of one to three months.

### Medium Term Forecasts

For minor strategic decisions related to the activity of the company, medium-term forecasts are made. They are critical in the field of business budgeting for the operating budget, and company budgets are designed on the basis of this forecast. Mid term forecast are required to forecast potential resources to purchase raw materials, hire personnel, or purchase machinery and equipment. A year is usually the time frame for a medium-term forecast.

### Long Term Forecasts

In strategic planning, they're used. Business opportunities, environmental factors, and internal resources must all be considered when making such decisions. Long-term forecasts are used to make major strategic decisions within an enterprise, and they are heavily influenced by resource considerations. They deal with complex concepts rather than specifics

Long term forecasts rely more heavily on government policy, social change, and technical change in their calculations. As a result, they are more concerned with general patterns and attempt to forecast revenue for periods longer than two years based on these trends.

## Data

A series of information, such as numbers, sentences, measurements, observations, or simple explanations of objects, is referred to as **data**. Data are quantifiable units of information gained by observation. **Quantitative and qualitative** data are the two main types of data, and both are equally relevant.

Classification of data based on the type of data collected

### 1. Cross-sectional data

Consider the information gathered on movies in 2017, such as budget, box office receipts, stars, directors, and film genre. Data is collected on various variables of interest over a long period â€“ CROSS-SECTIONAL DATA is a form of data like this.

### 2. Time series data

This data obtained for a single variable over multiple periods (e.g., demand for smartphones over multiple time intervals such as weekly, monthly, and yearly)

### 3. Panel data

This data is collected on a variety of variables over a long period, such as GDP, Gini index, and the unemployment rate for several countries for several years.

## Categories of Forecasting Method

### Qualitative

Where historical data is unavailable, qualitative forecasting approaches are sufficient. They are subjective, based on consumer and expert perception and decision.

### Quantitative

Forecasting future data as a result of past data is achieved using quantitative forecasting models. If historical numerical data is available and fair to conclude that some of the data trends will continue, they are suitable to use.

## Time-Series Analysis

A time series is made up of the four basic elements mentioned below:

- Basic or Secular or Long-time trend;
- Seasonal variations;
- Business cycles or cyclical movement; and
- Erratic or Irregular fluctuations.

The below graph shows sales values for the year 1986 to 2000. Its time-series analysis.

## Forecasting Variables

When dealing with time series, there are a variety of other variables to remember.

### Stationary

The property of stationarity is important in time series analysis. A time series is said to be stationary if its statistical properties do not change over time. In other words, the mean and variance are constant, and the covariance is independent by time.

### Seasonality

Seasonality refers to variations that occur regularly. For example, electricity consumption is high during the day and low at night, or online sales increase during the Christmas season before slowing down.

### Autocorrelated

The similarity between observations as a function of the time lag between them is known as autocorrelation.

## Time Series Analysi**s Models **

The two models that we usually use to decompose time series into their four components are as follows. The aim is to quantify and isolate the four forms of variations, as well as to evaluate their relative impact on the overall behaviour of the time series.

### Additive model

In the additive model, a single observation in a time series is represented by the sum of these four components.

**O = T + S + C + I**

where O represents the original data, T represents the trend. S represents the seasonal variations, C represents the cyclical variations, and I represent the irregular variations. In the additive model, the terms O, T, S, C, and I represent the terms.

### Multiplicative model

Model of Multiplication four elements in this model have a multiplicative relationship. As a result, we interpret a single observation in a time series as the sum of these four elements:

** O = T Ã— S Ã— C Ã— I**

## Forecasting Methods

Financial analysts use four different **forecasting methods** to estimate a company's projected profits, expenditures, and capital costs.

### Autoregressive (AR)

When a time series is regressed on previous values from the same time series, an autoregressive model is created.

In this regression model, the previous time period's response variable has become the predictor, and the errors follow our usual error assumptions in a simple linear regression model. An autorepression's order is the number of immediately preceding values in the series that are used to predict the current value. As a result, the preceding model is a first-order autoregression, written as AR(1).

It is worth noting that the equation relies on **t-1** and so on until t-n for a prediction of time t. This is known as a **lag prediction** because it is based on data points from the previous period of time.

The autoregressive model is a **stochastic process** that involves some degree of data randomness over time. The randomness (or fluctuations) indicates that you may be able to predict future trends with high accuracy using past data, but not with 100 percent accuracy.

### Moving Average (MA)

A moving average model uses past forecast errors in a regression-like model rather than using past forecast values in a regression.

y_{t}=c+Îµ_{t}+Î¸_{1}Îµ_{tâˆ’1}+Î¸_{2}Îµ_{tâˆ’2}+â‹¯+Î¸_{q}Îµ_{tâˆ’q},

Where Îµ_{t }is white noise, we refer to this as an **MA(**q**) model**, a moving average model of order q. It is worth noting that each value of y_{t} can be thought of as a weighted moving average of the previous few forecast errors. A time series model that accounts for very short-run autocorrelation is the moving average model. It essentially states that the next observation is the mean of all previous observations. The moving average model's order, q, can usually be estimated by inspecting the time series' ACF plot.

### Autoregressive Moving Average (ARMA)

An ARMA model, or Autoregressive Moving Average model, is used to describe weakly stationary stochastic time series in terms of two polynomials. The first of these polynomials is for autoregression, the second for the moving average.

Often this model is referred to as the **ARMA (p, q) model**; where:

- p is the order of the autoregressive polynomial,
- q is the order of the moving average polynomial.

The equation is given by:

Where:

Ï† = the autoregressive modelâ€™s parameters

Î¸ = the moving average modelâ€™s parameters

c = a constant

Î£ = summation notation

Îµ = error terms (white noise).

### Autoregressive Integrated Moving Average (ARIMA)/Box-Jenkins Models

ARIMA modelling (also known as Box-Jenkins modelling) is a method for simulating ARIMA processes mathematical models used for forecasting. To forecast future values, the method employs previous time-series data plus an error. It combines a general autoregressive model AR(p) with a general moving average model MA(q):

- AR(p)â€” uses previous values of the dependent variable to make predictions.
- MA(q)â€”uses the series mean and previous errors to make predictions.

The approach was first proposed by Box and Jenkins (1970), who detailed ARIMA's estimation and prediction procedures (Hyndman et al., 2008).

Nonseasonal Autoregressive Integrated Moving Average (Nonseasonal Autoregressive Integrated Moving Average) Three factors differentiate average models.

p = number of autoregressive terms,

d = how many nonseasonal differences are needed to achieve stationarity,

q = number of lagged forecast errors in the prediction equation.

### Exponential Smoothing (ES)

The exponential smoothing algorithm is used to generate a relatively smooth time series forecasting trend by exponentially decreasing the weight of older data values, resulting in weighted averages. To optimize model performance to a slowly varying mean, the smoothing degree (the width of the moving average) is adjusted.

The simplest form of exponential smoothing can be expressed as below:

**Î±** is the degree of smoothing ranging 0 < *Î±* < 1

Depending on how the analysis is configured, there is frequently a significant trade-off between retaining current observations and remaining constant.

## Common Mistakes

- Using unreliable product timing information
- Inaccurately predicting market adoption rates
- Not responding quickly enough (or being able to respond) to changing market conditions

## Context and Applications

- This topic is significant in the professional exams for both undergraduate and graduate courses, especially for computer engineering
- Economic Forecasting
- Sales Forecasting
- Budgetary Analysis
- Stock Market Analysis
- Yield Projections
- Inventory Studies

## Related Concepts

- Random Walk
- Residual Analysis
- Sample Autocorrelation Function

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