mindmap
root((Time Series Analysis))
Databases
TimeScaleDB
InfluxDB
Python tools
Altair
Pandas
DuckDB
Polars
Scipy
Gekko
Matplotlib
Core concepts
Trend
Cycle
Variation
Statistical movements
Stationary and non-stationary
Seasonality
Auto-Correlation
Forcasting
Auto Regressive Integrated Moving Average - ARIMA
Exponential smoothing
A mindmap of time series analysis
Core concepts explained visually
Time series
Observed values of the same variable collected at regular time intervals.
In the below example, revenue is the variable observed with a monthly time intervals given a year.
---
config:
xyChart:
width: 700
height: 350
themeVariables:
xyChart:
titleColor: "#ff0000"
---
xychart-beta
title "Sales revenue"
x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
y-axis "Revenue (in $)" 4000 --> 13000
line [5000, 6200, 7900, 8800, 10300, 11500, 12200, 11600, 10800, 10300, 9000, 8200]
Time series analysis
The method of analyzing a timestamped dataset to observe/forecast/predict past and future values for the observed variable. Hence this analysis can be used as a decision support system.
Trend
Positive secular trend
---
config:
xyChart:
width: 700
height: 350
themeVariables:
xyChart:
titleColor: "#ff0000"
---
xychart-beta
title "Sales revenue (positive secular trend)"
x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
y-axis "Revenue (in $)" 4000 --> 13000
line [5000, 5200, 6100, 5900, 6800, 7500, 8200, 7900, 8600, 8400, 9100, 9500]
Negative secular trend
---
config:
xyChart:
width: 700
height: 350
themeVariables:
xyChart:
titleColor: "#ff0000"
---
xychart-beta
title "Sales revenue (negative secular trend)"
x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
y-axis "Revenue (in $)" 4000 --> 20000
line [14000, 13600, 13900, 13200, 13500, 12800, 13100, 12500, 12700, 12100, 11800, 11500]
Seasonality
Time series data can change depending on the seasons/seasonal pattern.
Seasonal positive secular trend
---
config:
xyChart:
width: 700
height: 350
themeVariables:
xyChart:
titleColor: "#ff0000"
---
xychart-beta
title "Sales revenue (seasonal postive secular trend)"
x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
y-axis "Revenue (in $)" 4000 --> 20000
line [14000, 13600, 14800, 14200, 15100, 15600, 15300, 14900, 15800, 15400, 15900, 16200]
Seasonal negative secular trend
---
config:
xyChart:
width: 700
height: 350
themeVariables:
xyChart:
titleColor: "#ff0000"
---
xychart-beta
title "Sales revenue (seasonal negative secular trend)"
x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
y-axis "Revenue (in $)" 4000 --> 20000
line [14000, 13200, 13900, 12800, 13500, 14100, 12600, 13200, 13800, 12400, 12900, 13300]
Cyclic
---
config:
xyChart:
width: 700
height: 350
themeVariables:
xyChart:
titleColor: "#ff0000"
---
xychart-beta
title "Sales revenue (Cyclic trend)"
x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
y-axis "Revenue (in $)" 4000 --> 20000
line [10000, 10800, 11900, 13200, 14300, 15100, 15500, 15400, 14800, 13900, 12800, 11700]
Resources
Here are some of the resources which helped me learn the basic concepts of time series analysis with no specific order.
Introduction to time series analysis
Lecture on time series analysis
Patterns and trends in time series plots
When I learn an interesting aspect of time series analysis, I will update this post. For now, time series analysis was fun learning. I have barely scratched the surface here.
More fun to be had!