Notes
Introduction to Time Series and Forecasting
Definition
A time series is a sequence of observations recorded
at different points of time, usually in chronological order.
The observations may be collected daily, monthly, quarterly,
yearly, or at any other regular time interval.
Example
A company's monthly sales for January, February, March and April
form a time series.
Working
The observations are arranged according to time so that we can study
how the variable changes. This helps us identify useful patterns
that may later help in forecasting future values.
Time Series Forecasting
Time series forecasting is the process of using past
and present observations to estimate future values of a variable.
It is useful when future outcomes are expected to depend, at least
partly, on historical patterns.
Example
A shop can use previous monthly sales to estimate next month's sales.
Basic Forecasting Flow
Past Data
↓
Identify Pattern
↓
Build Forecasting Model
↓
Estimate Future Value
Models for Time Series Analysis
A time series model is a mathematical or statistical
representation used to describe the behaviour of observations over
time. The model helps identify patterns and can be used for analysis
and forecasting.
Example
Past sales data can be modeled to estimate future sales.
Observed Time Series
↓
Identify Structure
↓
Choose Model
↓
Estimate Parameters
↓
Check Model
↓
Forecast
Two broad approaches are commonly used at this stage:
-
Time-series-based models:
the forecast depends mainly on the past values of the same series.
Example: using previous monthly sales values to forecast future sales.
-
Regression-based models:
the forecast also uses related explanatory variables.
Example: predicting electricity demand using temperature and
historical demand.
Exam Note
Detailed ARMA and ARIMA mathematics belong to later units.
Unit 1 only requires the idea of a model and these two broad approaches.
Nature and Uses of Forecasting
Forecasting is an estimation of what may happen in
the future based on available historical information, current
conditions, and an appropriate forecasting method.
A forecast is an estimate, not a guaranteed future value.
Example
A company estimating next quarter's demand based on previous sales.
Uses of Forecasting
- Business: sales and demand estimation
- Finance: revenue and financial planning
- Inventory: stock requirement estimation
- Production: production planning
- Government: planning and resource allocation
- Weather: future weather estimation
- Energy: electricity demand forecasting
Forecasting Process
The forecasting process is a systematic sequence of
activities used to convert historical data into useful future estimates.
Example
Forecast monthly sales for the next six months.
-
Define the Forecasting Problem:
state clearly what is to be forecast, for which period, and why
the forecast is needed.
-
Collect Data:
gather historical observations and any related information needed
for the problem.
-
Prepare and Understand Data:
check the series, study its pattern, and correct missing or
incorrect values where possible.
-
Select Forecasting Method:
choose a suitable time-series-based or regression-based approach.
-
Build the Model:
fit the selected method to the prepared data.
-
Evaluate the Model:
check whether the model describes the past data reasonably well.
-
Generate Forecast:
use the accepted model to estimate future values.
-
Monitor Forecast Performance:
compare later actual values with the forecast and revise the
method if needed.
Data for Forecasting
Forecasting depends on suitable and reliable data. The quality,
relevance, frequency and length of historical data can strongly
affect the usefulness of a forecasting model.
-
Historical Data:
previous observations of the variable, such as five years of
monthly sales.
-
Frequency:
how often values are recorded, such as hourly, daily, monthly
or yearly. Example: hourly or daily electricity demand.
-
Data Quality:
missing, incorrect or inconsistent values reduce the reliability
of the forecast.
-
Relevant Variables:
additional information that helps explain the series, such as
temperature in electricity-demand forecasting.
Resources for Forecasting
Forecasting resources include the data, people, methods, software,
computational facilities and domain knowledge required to produce
and evaluate forecasts.
Forecasting Resources
|
├── Historical Data
├── Statistical Methods
├── Software / Tools
├── Computational Resources
├── Domain Knowledge
└── Skilled Analysts
- Historical Data: the recorded series used for modelling.
- Statistical Methods: the techniques used to identify patterns and make estimates.
- Software / Tools: programs used to analyse data and generate forecasts.
- Computational Resources: the computing facilities needed to process the data.
- Domain Knowledge: subject understanding, such as sales, weather or energy demand.
- Skilled Analysts: people who can prepare data, choose methods and interpret results.