Time Series Forecasting. Introduction and beginner-friendly… | by Jemish Vakharia | Jul, 2025

What’s Time Sequence Forecasting?

Time: Refers to knowledge collected over a steady interval or at distinct time factors.

Sequence: Implies that the information factors are organized in a sequential order.

Forecasting: The method of utilizing previous knowledge to make predictions concerning the future.

Not like conventional datasets, the order issues in time sequence.

Why Do We Forecast?

Each firm or group operates beneath a mixture of inside and exterior elements — competitors, technological modifications, inflation, coverage shifts, and even sudden crises. Correct forecasting helps companies:

• Put together for future dangers and alternatives.
• Make knowledgeable choices backed by knowledge traits.
• Consider previous methods and modify accordingly.

Briefly, forecasting is not only concerning the future but in addition about studying from the previous.

Kinds of Knowledge Constructions

1. Cross-sectional knowledge: Captured from a number of entities at a single time limit. Instance: Earnings ranges of 100 folks surveyed in 2022.
2. Time sequence knowledge: Captured from a single entity over a number of time factors. Instance: Day by day closing costs of Apple inventory from 2010 to 2020.
3. Panel knowledge: A hybrid — knowledge collected from a number of entities over a number of time durations. Instance: Quarterly gross sales knowledge of 10 corporations over 5 years.
4. Naïve or unstructured knowledge: Usually utilized in fields like NLP or laptop imaginative and prescient; consists of knowledge like pictures, movies, and uncooked textual content that don’t observe a tabular format.

Parts of a Time Sequence

Time sequence knowledge is often composed of 4 fundamental parts:

1. Pattern: The long-term motion within the knowledge, both upward, downward, or flat. Instance: An organization’s steadily rising income over 10 years.
2. Seasonality: Patterns that repeat at common, short-term intervals (typically yearly or quarterly). Instance: Greater ice cream gross sales throughout summer season months.
3. Cyclicity: Fluctuations that happen over longer, irregular time spans — typically tied to financial or enterprise cycles. Instance: A recession each 5–10 years.
4. Irregularity (Noise): Random, unpredictable variations within the knowledge brought on by one-off occasions. Instance: A sudden drop in inventory costs attributable to a pure catastrophe.

Relying on how the parts mix, time sequence will be modeled in two widespread methods:

1. Additive Mannequin: Yt = Pattern + Seasonality + Noise
2. Multiplicative Mannequin: Yt = Pattern × Seasonality × Noise

The selection between the 2 is determined by whether or not the seasonal results and noise stay fixed (additive) or change with the extent of the sequence (multiplicative).

Instance:

In additive, if gross sales sometimes enhance by 10,000 every December, this seasonal increase stays the identical whether or not the baseline gross sales are 50,000 or 500,000.

Whereas in multiplicative, if gross sales sometimes enhance by 20% every December, a retailer with 50,000 baseline gross sales would see a ten,000 increase, whereas a retailer with 500,000 baseline would see a 100,000 enhance.

Pre-requisites for Time Sequence Forecasting

Earlier than leaping into modeling, it’s essential to make sure that the dataset meets just a few essential circumstances.

1. Numeric Knowledge Solely – Time sequence fashions work with numerical values. Categorical knowledge (like metropolis names or product classes) have to be both excluded or correctly encoded earlier than modeling.
2. Right Knowledge Varieties – Make sure the time column is in correct datetime format and that the goal variable is numeric. Incorrect varieties can break even the only forecasting fashions.
3. No Lacking Timestamps – Lacking values in a time sequence can distort traits or seasonal patterns. If the information has gaps in dates or lacking values, imputation is essential — whether or not by forward-filling, interpolation, or domain-specific strategies.
4. Sequential Order Issues – Time sequence knowledge have to be sorted in ascending chronological order. Any shuffling or dysfunction within the sequence invalidates the temporal relationships, that are the core of time sequence evaluation.
5. Consciousness of Knowledge Patterns – Perceive whether or not your knowledge reveals development, seasonality, noise, or abrupt shifts. This understanding will assist information us alternative of forecasting mannequin in a while.

1. Smoothing Fashions (Nineteen Fifties–Sixties)

These are early forecasting strategies that depend on averaging previous observations to foretell future values. Finest used when the information exhibits no development or seasonality. Whereas hardly ever used in the present day in isolation, they function foundational ideas for extra superior fashions.

2. Holt’s Linear Pattern Methodology (1957)

Often known as double exponential smoothing, it accounts for development however assumes no seasonality within the knowledge.

3. Holt-Winters Methodology (1960)

Additionally known as triple exponential smoothing, this mannequin captures each development and seasonality, making it appropriate for extra complicated time sequence.

4. AR Mannequin (Auto-Regressive) (Early foundations in Twenties–Nineteen Forties)

Forecasts the longer term primarily based by itself earlier values. It assumes that previous lags of the sequence have a linear affect on the present worth.

5. MA Mannequin (Transferring Common) (Developed alongside AR, formalized in 1938)

Makes use of previous forecast errors to foretell future values. It smooths the sequence by averaging out the noise from residuals.

6. ARMA (Auto-Regressive Transferring Common) (1970)

A mix of AR and MA fashions, used when the time sequence is stationary however exhibits dependencies in each previous values and previous errors.

7. ARIMA (Auto-Regressive Built-in Transferring Common) (1970)

An extension of ARMA that features differencing (Built-in) to deal with non-stationary knowledge. One of the crucial extensively used classical fashions for time sequence forecasting.

8. ARIMAX (ARIMA with Exogenous Variables) (Seventies-Nineteen Eighties)

Enhances ARIMA by incorporating exterior variables that will affect the forecast. For instance, predicting gasoline costs utilizing each historic costs and crude oil charges.

9. SARIMA (Seasonal ARIMA) (1970)

Builds on ARIMA to incorporate seasonal patterns. Helpful when the information reveals repeating cycles resembling month-to-month or yearly traits.

10. SARIMAX (Seasonal ARIMA with Exogenous Variables) (Nineteen Eighties-Nineties)

Probably the most complete amongst classical fashions, it handles seasonality and exterior elements concurrently — ultimate for real-world enterprise or financial forecasting.

Core Parameters of Time Sequence Fashions (ARIMA or SARIMA):

In time sequence modeling, p, d, and q are key parameters utilized in ARIMA and SARIMA fashions:

• p – Autoregression
  The variety of previous values to contemplate.
  We are able to consider it as “What number of earlier time steps affect the present one?”
• d – Differencing
  The variety of occasions the information must be differenced to take away traits. Used to make the information stationary.
• q – Transferring Common
  The variety of previous forecast errors to incorporate.
  It’s like: “How a lot ought to we appropriate primarily based on previous errors?”

For seasonal time sequence, we additionally use P, D, Q— which symbolize the identical concepts, however utilized throughout seasonal cycles (like yearly or quarterly patterns), together with a seasonal interval s.

1. Load and Clear the Knowledge

• Import the dataset and guarantee all null values are dealt with appropriately (for instance: via interpolation or ahead/backward fill).
• Make sure the datetime column is within the appropriate format and set it because the index.
• Guarantee the information is sorted in ascending chronological order

2. Decompose the Time Sequence

• Use the seasonal_decompose() perform to visualise the development, seasonality, and residuals.
• The development exhibits the general route of the information over time, seasonality reveals repeating patterns at fastened intervals (like yearly or month-to-month cycles), and residuals spotlight the random noise left after eradicating development and seasonality.
• By analyzing these plots, we will determine whether or not the sequence wants differencing, seasonal adjustment, or smoothing earlier than making use of forecasting fashions.

3. Examine for Autocorrelation

• Apply the Durbin-Watson take a look at to detect autocorrelation in residuals.
• A worth near 2 suggests no autocorrelation (presumably not a time sequence drawback).
• A worth a lot decrease or greater than 2 signifies autocorrelation and confirms time-dependent construction.

4. Take a look at for Stationarity

• Use the Augmented Dickey-Fuller (ADF) take a look at:
• If p-value < 0.05, the information is stationary.
• If not, apply differencing to take away traits and make the sequence stationary.

Differencing Strategy:

• Create a brand new column with the distinction between present and former time steps (first-order distinction) and verify.
• If nonetheless non-stationary, repeat the method (second-order differencing).
• This variety of occasions you distinction the information is your d (or D) worth in ARIMA/SARIMA fashions.

For Seasonal Differencing: Subtract the worth from the identical level within the earlier season (e.g., present month minus worth 12 months in the past for yearly seasonality)

5. Decide Mannequin Parameters (p, d, q)

• Use the PACF (Partial Autocorrelation Perform) plot to search out p (variety of AR phrases).
• Use the ACF (Autocorrelation Perform) plot to search out q (variety of MA phrases).
• Rely the variety of important spikes outdoors the shaded space earlier than the plot cuts again inside — this provides usp or q.

6. Construct and Match the Mannequin

• Use a mannequin like SARIMAX or ARIMA:
• Outline order = (p, d, q)
• If utilizing seasonality, set seasonal_order = (P, D, Q, interval)

7. Consider Mannequin Efficiency

• Use metrics like AIC (Akaike Info Criterion) and BIC (Bayesian Info Criterion) — decrease values point out a better-fitting mannequin.
• Additionally evaluate forecasted values with actuals visually utilizing a plot. An in depth alignment signifies good efficiency.

Automate Hyperparameter Tuning

Guide tuning will be tedious. We are able to automate the method by:

• Making a parameter grid utilizing libraries like itertools
• Looping via combos and coaching fashions for every.
• Evaluating fashions utilizing a metric like AIC to establish one of the best configuration.

Automating Mannequin Choice with auto_arima

Whereas manually tuning ARIMA parameters (p, d, q) and seasonal parts is academic, it may be time-consuming and error-prone. That’s the place auto_arima from the pmdarima library is available in.

This perform automates:

• Detecting stationarity and differencing wants
• Choosing optimum values for p, d, q (and optionally P, D, Q)
• Evaluating fashions primarily based on AIC, BIC, or different scoring metrics

Key Parameters:

• seasonal: True in case your knowledge has seasonality
• m: Seasonal interval (e.g., 12 for month-to-month knowledge with yearly seasonality)
• Parameters to set- mannequin : ‘additive’ or ‘multiplicative’ , interval : variety of time steps in a single seasonal cycle (e.g., 12 for month-to-month knowledge with yearly seasonality)

Prophet is an open-source forecasting device developed by Fb, designed for dealing with time sequence knowledge with robust seasonality, development modifications, holidays, and outliers.

Key Options:

• Routinely fashions development, seasonality, holidays, and abrupt modifications (outliers).
• Handles lacking knowledge and non-linear traits properly.
• Requires minimal tuning — ultimate for fast prototyping.

Knowledge Format:

Prophet expects two columns in a dataset:

• ds : Date column (in datetime format)
• y : Goal variable to forecast

Not like ARIMA, Prophet doesn’t require you to manually set p, d, and q. It’s thought-about extra of a black field — nice for ease of use, however with much less management over inside mechanics.

Darts is a robust Python library developed by Unit8 that gives a unified interface for a variety of forecasting fashions — from classical statistical fashions (like ARIMA, Exponential Smoothing) to machine studying and deep studying fashions (like XGBoost, RNN, LSTM, and Transformer-based fashions).

Key Options:

• Helps univariate and multivariate time sequence.
• Permits mannequin ensembling, probabilistic forecasting, and backtesting.
• Simplifies preprocessing, scaling, and analysis utilizing built-in utilities.

Preprocessing Notes:

Earlier than utilizing deep studying or ML-based fashions in Darts:

• Guarantee the information is constant — e.g., convert all financial values to the identical foreign money if wanted.
• Apply scaling to normalize your sequence (particularly for neural networks).

Darts presents built-in preprocessing instruments to deal with this effectively.

Time sequence forecasting is a robust device for making sense of patterns over time — whether or not we’re predicting gross sales, inventory costs, or seasonal demand. On this put up, we explored its elementary parts, preprocessing steps, mannequin choice (ARIMA, SARIMA), and even trendy instruments like Fb Prophet and Darts.

Understanding how traits, seasonality, and noise work together helps construct stronger, extra dependable fashions. Whether or not we’re simply beginning out or refining forecasting abilities, the easiest way to study is by making use of these strategies to real-world datasets.