I to keep away from time collection evaluation. Each time I took a web based course, I’d see a module titled “Time Collection Evaluation” with subtopics like Fourier Transforms, autocorrelation capabilities and different intimidating phrases. I don’t know why, however I all the time discovered a cause to keep away from it.
However right here’s what I’ve realized: any advanced matter turns into manageable after we begin from the fundamentals and deal with understanding the instinct behind it. That’s precisely what this weblog collection is about : making time collection really feel much less like a maze and extra like a dialog together with your information over time.
We perceive advanced subjects rather more simply once they’re defined by way of real-world examples. That’s precisely how I’ll method this collection.
In every publish, we’ll work with a easy dataset and discover what’s wanted from a time collection perspective. We’ll construct instinct round every idea, perceive why it issues, and implement it step-by-step on the info.
Time Collection Evaluation is the method of understanding, modeling and Forecasting information that’s noticed over time. It includes figuring out patterns resembling tendencies, seasonality and noise utilizing previous observations to make knowledgeable predictions about future values.
Let’s begin by contemplating a dataset named Daily Minimum Temperatures in Melbourne (). This dataset comprises day by day data of the bottom temperature (in Celsius) noticed in Melbourne, Australia, over a 10-year interval from 1981 to 1990. Every entry contains simply two columns:
Date: The calendar day (from 1981-01-01 to 1990-12-31)
Temp: The minimal temperature recorded on that day
You’ve in all probability heard of fashions like ARIMA, SARIMA or Exponential Smoothing. However earlier than we go there, it’s a good suggestion to check out some easy baseline fashions first, to see how effectively a primary method performs on our information.
Whereas there are lots of varieties of baseline fashions utilized in time collection forecasting, right here we’ll deal with the three most important ones, that are easy, efficient, and extensively relevant throughout industries.
Naive Forecast: Assumes the subsequent worth would be the identical because the final noticed one.
Seasonal Naive Forecast: Assumes the worth will repeat from the identical level final season (e.g., final week or final month).
Transferring Common: Takes the typical of the final n factors.
You is likely to be questioning, why use baseline fashions in any respect? Why not simply go straight to the well-known forecasting strategies like ARIMA or SARIMA?
Let’s take into account a store proprietor who needs to forecast subsequent month’s gross sales. By making use of a transferring common baseline mannequin, they’ll estimate subsequent month’s gross sales because the common of earlier months. This straightforward method would possibly already ship round 80% accuracy — ok for planning and stock selections.
Now, if we change to a extra superior mannequin like ARIMA or SARIMA, we would enhance accuracy to round 85%. However the important thing query is: is that further 5% well worth the further time, effort and sources? On this case, the baseline mannequin does the job.
In truth, in most on a regular basis enterprise eventualities, baseline fashions are adequate. We usually flip to classical fashions like ARIMA or SARIMA in high-impact industries resembling finance or power, the place even a small enchancment in accuracy can have a big monetary or operational influence. Even then, a baseline mannequin is normally utilized first — not solely to offer fast insights but additionally to behave as a benchmark that extra advanced fashions should outperform.
Okay, now that we’re able to implement some baseline fashions, there’s one key factor we have to perceive first:
Each time collection is made up of three predominant elements — development, seasonality and residuals.
Time collection decomposition separates information into development, seasonality and residuals (noise), serving to us uncover the true patterns beneath the floor. This understanding guides the selection of forecasting fashions and improves accuracy. It’s additionally a significant first step earlier than constructing each easy and superior forecasting options.
Pattern
That is the general path your information is transferring in over time — going up, down or staying flat.
Instance: Regular lower in month-to-month cigarette gross sales.
Seasonality
These are the patterns that repeat at common intervals — day by day, weekly, month-to-month or yearly.
Instance: Cool drinks gross sales in summer season.
Residuals (Noise)
That is the random “leftover” a part of the info, the unpredictable ups and downs that may’t be defined by development or seasonality.
Instance: A one-time automobile buy exhibiting up in your month-to-month expense sample.
Now that we perceive the important thing elements of a time collection, let’s put that into follow utilizing an actual dataset: Day by day Minimal Temperatures in Melbourne, Australia.
We’ll use Python to decompose the time collection into its development, seasonality, and residual elements so we will higher perceive its construction and select an acceptable baseline mannequin.
:
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import seasonal_decompose
# Load the dataset
df = pd.read_csv("minimal day by day temperatures information.csv")
# Convert 'Date' to datetime and set as index
df['Date'] = pd.to_datetime(df['Date'], dayfirst=True)
df.set_index('Date', inplace=True)
# Set an everyday day by day frequency and fill lacking values utilizing ahead fill
df = df.asfreq('D')
df['Temp'].fillna(technique='ffill', inplace=True)
# Decompose the day by day collection (365-day seasonality for yearly patterns)
decomposition = seasonal_decompose(df['Temp'], mannequin='additive', interval=365)
# Plot the decomposed elements
decomposition.plot()
plt.suptitle('Decomposition of Day by day Minimal Temperatures (Day by day)', fontsize=14)
plt.tight_layout()
plt.present()
Output:
The decomposition plot clearly exhibits a robust seasonal sample that repeats annually, together with a gentle development that shifts over time. The residual element captures the random noise that isn’t defined by development or seasonality.
Within the code earlier, you might need seen that I used an additive mannequin for decomposing the Time Series. However what precisely does that imply — and why is it the fitting selection for this dataset?
Let’s break it down.
In an additive mannequin, we assume Pattern, Seasonality and Residuals (Noise) mix linearly, like this:
Y = T + S + R
The place:
Y is the precise worth at time t
T is the development
S is the seasonal element
R is the residual (random noise)
This implies we’re treating the noticed worth because the sum of the elements, every element contributes independently to the ultimate output.
I selected the additive mannequin as a result of once I appeared on the sample in day by day minimal temperatures, I seen one thing vital:
The road plot above exhibits the day by day minimal temperatures from 1981 to 1990. We will clearly see a robust seasonal cycle that repeats annually, colder temperatures in winter, hotter in summer season.
Importantly, the amplitude of those seasonal swings stays comparatively constant through the years. For instance, the temperature distinction between summer season and winter doesn’t seem to develop or shrink over time. This stability in seasonal variation is a key signal that the additive mannequin is suitable for decomposition, for the reason that seasonal element seems to be impartial of any development.
We use an additive mannequin when the development is comparatively steady and doesn’t amplify or distort the seasonal sample, and when the seasonality stays inside a constant vary over time, even when there are minor fluctuations.
Now that we perceive how the additive mannequin works, let’s discover the multiplicative mannequin — which is usually used when the seasonal impact scales with the development which can even assist us perceive the additive mannequin extra clearly.
Contemplate a family’s electrical energy consumption. Suppose the family makes use of 20% extra electrical energy in summer season in comparison with winter. Meaning the seasonal impact isn’t a set quantity — it’s a proportion of their baseline utilization.
Let’s see how this seems with actual numbers:
In 2021, the family used 300 kWh in winter and 360 kWh in summer season (20% greater than winter).
In 2022, their winter consumption elevated to 330 kWh, and summer season utilization rose to 396 kWh (nonetheless 20% greater than winter).
In each years, the seasonal distinction grows with the development from +60 kWh in 2021 to +66 kWh in 2022 although the proportion enhance stays the identical. That is precisely the form of conduct {that a} multiplicative mannequin captures effectively.
In mathematical phrases:
Y = T ×S ×R
The place:
Y: Noticed worth
T: Pattern element
S: Seasonal element
R: Residual (noise)
By trying on the decomposition plot, we will determine whether or not an additive or multiplicative mannequin suits our information higher.
There are additionally different highly effective decomposition instruments obtainable, which I’ll be overlaying in one among my upcoming weblog posts.Now that we’ve got a transparent understanding of additive and multiplicative fashions, let’s shift our focus to making use of a baseline mannequin that matches this dataset.
Based mostly on the decomposition plot, we will see a robust seasonal sample within the information, which suggests {that a} Seasonal Naive mannequin is likely to be an excellent match for this time collection.
This mannequin assumes that the worth at a given time would be the identical because it was in the identical interval of the earlier season — making it a easy but efficient selection when seasonality is dominant and constant. For instance, if temperatures usually comply with the identical yearly cycle, then the forecast for July 1st, 1990, would merely be the temperature recorded on July 1st, 1989.
Code:
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
# Load the dataset
df = pd.read_csv("minimal day by day temperatures information.csv")
# Convert 'Date' column to datetime and set as index
df['Date'] = pd.to_datetime(df['Date'], dayfirst=True)
df.set_index('Date', inplace=True)
# Guarantee common day by day frequency and fill lacking values
df = df.asfreq('D')
df['Temp'].fillna(technique='ffill', inplace=True)
# Step 1: Create the Seasonal Naive Forecast
seasonal_period = 365 # Assuming yearly seasonality for day by day information
# Create the Seasonal Naive forecast by shifting the temperature values by twelve months
df['Seasonal_Naive'] = df['Temp'].shift(seasonal_period)
# Step 2: Plot the precise vs forecasted values
# Plot the final 2 years (730 days) of information to check
plt.determine(figsize=(12, 5))
plt.plot(df['Temp'][-730:], label='Precise')
plt.plot(df['Seasonal_Naive'][-730:], label='Seasonal Naive Forecast', linestyle='--')
plt.title('Seasonal Naive Forecast vs Precise Temperatures')
plt.xlabel('Date')
plt.ylabel('Temperature (°C)')
plt.legend()
plt.tight_layout()
plt.present()
# Step 3: Consider utilizing MAPE (Imply Absolute Share Error)
# Use the final twelve months for testing
check = df[['Temp', 'Seasonal_Naive']].iloc[-365:].copy()
check.dropna(inplace=True)
# MAPE Calculation
mape = np.imply(np.abs((check['Temp'] - check['Seasonal_Naive']) / check['Temp'])) * 100
print(f"MAPE (Seasonal Naive Forecast): {mape:.2f}%")Output:
To maintain the visualization clear and centered, we’ve plotted the final two years of the dataset (1989–1990) as an alternative of all 10 years.
This plot compares the precise day by day minimal temperatures in Melbourne with the values predicted by the Seasonal Naive mannequin, which merely assumes that every day’s temperature would be the identical because it was on the identical day one 12 months in the past.
As seen within the plot, the Seasonal Naive forecast captures the broad form of the seasonal cycles fairly effectively — it mirrors the rise and fall of temperatures all year long. Nevertheless, it doesn’t seize day-to-day variations, nor does it reply to slight shifts in seasonal timing. That is anticipated, because the mannequin is designed to repeat the earlier 12 months’s sample precisely, with out adjusting for development or noise.
To guage how effectively this mannequin performs, we calculate the Imply Absolute Share Error (MAPE) over the ultimate twelve months of the dataset (i.e., 1990). We solely use this era as a result of the Seasonal Naive forecast wants a full 12 months of historic information earlier than it may well start making predictions.
Imply Absolute Share Error (MAPE) is a generally used metric to judge the accuracy of forecasting fashions. It measures the common absolute distinction between the precise and predicted values, expressed as a proportion of the particular values.
In time collection forecasting, we usually consider mannequin efficiency on the most up-to-date or goal time interval — not on the center years. This displays how forecasts are utilized in the actual world: we construct fashions on historic information to foretell what’s coming subsequent.
That’s why we calculate MAPE solely on the closing twelve months of the dataset — this simulates forecasting for a future and provides us a practical measure of how effectively the mannequin would carry out in follow.
A MAPE of 28.23%, which supplies us a baseline stage of forecasting error. Any mannequin we construct subsequent — whether or not it’s custom-made or extra superior, ought to purpose to outperform this benchmark.
A MAPE of 28.23% signifies that, on common, the mannequin’s predictions had been 28.23% off from the precise day by day temperature values over the past 12 months.
In different phrases, if the true temperature on a given day was 10°C, the Seasonal Naïve forecast might need been round 7.2°C or 12.8°C, reflecting a 28% deviation.
I’ll dive deeper into analysis metrics in a future publish.
On this publish, we laid the muse for time collection forecasting by understanding how real-world information may be damaged down into development, seasonality, and residuals by way of decomposition. We explored the distinction between additive and multiplicative fashions, applied the Seasonal Naive baseline forecast and evaluated its efficiency utilizing MAPE.
Whereas the Seasonal Naive mannequin is straightforward and intuitive, it comes with limitations particularly for this dataset. It assumes that the temperature on any given day is similar to the identical day final 12 months. However because the plot and MAPE of 28.23% confirmed, this assumption doesn’t maintain completely. The info shows slight shifts in seasonal patterns and long-term variations that the mannequin fails to seize.
Within the subsequent a part of this collection, we’ll go additional. We’ll discover methods to customise a baseline mannequin, evaluate it to the Seasonal Naive method and consider which one performs higher utilizing error metrics like MAPE, MAE and RMSE.
We’ll additionally start constructing the muse wanted to grasp extra superior fashions like ARIMA together with key ideas resembling:
- Stationarity
- Autocorrelation and Partial Autocorrelation
- Differencing
- Lag-based modeling (AR and MA phrases)
Half 2 will dive into these subjects in additional element, beginning with customized baselines and ending with the foundations of ARIMA.
Thanks for studying. I hope you discovered this publish useful and insightful.
