Time Series Forecasting on Sales Data

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1.Understand the Basics of Time Series

•A time series is a sequence of data points collected or recorded at time intervals. •Components include: Trend: Long-term movement in data. Seasonality: Repeating short-term cycles. Cyclic patterns: Irregular long-term fluctuations. Noise: Random variation.

1. Trend – The Long-Term Direction of Data

Meaning:

A trend is the general movement of data over a long period. It shows whether the values are increasing, decreasing, or staying constant over time.

Example:

Imagine an online store where monthly sales go from $10,000 to $50,000 over three years. Even if there are some up-and-down fluctuations month to month, the overall direction is upward. That's an upward trend.

Real-life examples:

Housing prices increasing steadily over 10 years.

A growing number of users on a social media app.

2. Seasonality – Short-Term Repeating Patterns

Meaning:

Seasonality refers to regular, predictable patterns that happen at specific time intervals, like daily, weekly, monthly, or yearly.

Example:

Ice cream sales increase every summer and decrease every winter.

Online shopping spikes during Black Friday, Christmas, or Chinese New Year every year.

These patterns are consistent and repeat due to weather, holidays, or human behavior.

3. Cyclic Patterns – Irregular Long-Term Fluctuations

Meaning:

A cyclical pattern is a wave-like movement in the data that occurs over the long term, but not at fixed intervals like seasonality. These are usually driven by economic or market conditions.

Example:

The economy goes through booms and recessions, but we can't say they happen exactly every 3 years.

Stock markets rise and fall in cycles, but the timing isn't predictable.

Difference from Seasonality:

Seasonality is fixed (e.g., every December).

Cycles are not fixed and often hard to predict.

4. Noise – Random, Unpredictable Fluctuations

Meaning:

Noise refers to random variations in the data that don’t follow any pattern. It's caused by unexpected events, errors, or anomalies.

Example:

A restaurant’s sales suddenly drop one day because of road construction nearby.

A data entry mistake causes an incorrect sales value to appear.

Noise is what we try to filter out during analysis because it’s unpredictable and not meaningful in the long term.

Summary Table:

Component	Time Scale	Predictable?	Example
Trend	Long-term	Yes	Sales growing over 3 years
Seasonality	Short-term, fixed cycles	Yes	Higher sales during summer every year
Cyclic	Long-term, irregular cycles	Partially	Economic recession and recovery cycles
Noise	Any time	No	Sales dip due to a one-day power outage

2.Prepare the Sales Data

•Ensure your data is clean, with consistent date formatting. •Remove duplicates, fill or handle missing values. •Aggregate to the desired frequency (daily, weekly, monthly).

date	sales	year	month	day	weekday	week	is_weekend	is_month_end
2019-09-09	1200	2019	9	9	0	37	0	0
2019-09-10	1300	2019	9	10	1	37	0	0
2019-09-11	1100	2019	9	11	2	37	0	0

Column	Purpose	Use in Analysis
`date`	Main time index	Identify trends, seasonality, and forecast sales.
`sales`	Sales value for the specific day	Analyze trends, seasonality, and forecast sales.
`year`	Year part of the date	Compare sales year-over-year.
`month`	Month part of the date	Analyze monthly seasonality and trends.
`day`	Day of the month	Identify patterns for specific days of the month.
`weekday`	Day of the week (0=Monday, 6=Sunday)	Identify weekday vs weekend sales patterns.
`week`	Week number of the year	Track trends or seasonality on a weekly basis.
`is_weekend`	Indicator for weekends (1=Yes, 0=No)	Analyze if weekends have higher sales.
`is_month_end`	Indicator for month-end (1=Yes, 0=No)	Examine month-end effects (e.g., promotions, last-minute sales).

3.Visualize the Data

•Plot line graphs to observe trends and seasonality. •Use moving averages or decomposition to separate components.

4.Stationarize the Series

•Most models require a stationary time series (constant mean/variance). •Use differencing or log transformation to make it stationary. •Check stationarity with the ADF test (Augmented Dickey-Fuller).

Differencing is a technique used to make a time series stationary by removingits trend component. It works by computing the difference between each data point and its previous one, thereby eliminating long-term trends such as consistent increases or decreases in the data.

Log transformation is used when your data shows changing variance — for example, when fluctuations get bigger as values increase. Taking the logarithm compresses the scale of large values and stabilizes variance.

Model	Requires Stationary Data?	Reason	How to Make Stationary (if needed)
ARIMA / SARIMA	Yes	Assumes constant mean and variance, and requires stationary data for proper modeling.	Differencing, Log Transformation
LSTM / GRU (Deep Learning)	No	Can capture trends and seasonality directly from the data, even if it’s non-stationary.	Optional: Stationary data can help improve performance.
XGBoost / LightGBM (Tree Models)	No	Can handle non-stationary data as long as proper time-based features are included.	Feature engineering (time-based features like month, week).
Prophet	No	Handles trend and seasonality internally; no need to make the data stationary.	Optional: Stationary data can be used for improved results.

5.Choose a Forecasting Model

Common models include: •ARIMA (AutoRegressive Integrated Moving Average) •SARIMA (Seasonal ARIMA) •Prophet (Facebook’s model for trend/seasonality) •LSTM (for deep learning-based forecasting) •XGBoost or LightGBM with time features

Sales Forecast for Next 12 Months: ds yhat yhat_lower yhat_upper 48 2017-12-31 5140.288248 2657.765329 7442.897327 49 2018-01-31 4183.106428 1756.435972 6345.867659 50 2018-02-28 7548.698781 5307.431892 9923.442633 51 2018-03-31 3028.596319 670.286161 5353.491328 52 2018-04-30 5681.844430 3419.796569 7947.527499 53 2018-05-31 9623.025053 7407.128556 12210.501998 54 2018-06-30 12114.798430 9959.973203 14496.319345 55 2018-07-31 -347.569620 -2664.352405 1832.156175 56 2018-08-31 12416.723603 9963.292354 14761.788088 57 2018-09-30 11983.319951 9783.522730 14524.616427 58 2018-10-31 12056.335799 9619.594019 14287.291458 59 2018-11-30 13705.830357 11469.002839 16079.450986