📈 MemoLearning Time Series Analysis

Analyze temporal patterns and build forecasting models for time-dependent data

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Time Series Analysis Curriculum

12
Core Units
~75
TS Techniques
15+
Models
30+
Applications
1

Time Series Fundamentals

Understand the basic concepts of time series data and its unique characteristics.

  • What is time series data
  • Temporal dependence
  • Types of time series
  • Time series components
  • Stationarity concepts
  • Seasonality patterns
  • Data collection considerations
  • Common applications
2

Time Series Decomposition

Learn to decompose time series into trend, seasonal, and residual components.

  • Additive vs multiplicative models
  • Trend extraction methods
  • Seasonal decomposition
  • Classical decomposition
  • STL decomposition
  • X-13ARIMA-SEATS
  • Residual analysis
  • Interpretation of components
3

Exploratory Time Series Analysis

Explore time series data using visualization and descriptive statistics.

  • Time series plotting
  • Autocorrelation functions
  • Partial autocorrelation
  • Cross-correlation analysis
  • Lag plots
  • Periodogram analysis
  • Summary statistics
  • Outlier detection
4

Stationarity and Preprocessing

Learn about stationarity requirements and preprocessing techniques for time series.

  • Stationarity definition
  • Unit root tests
  • Augmented Dickey-Fuller test
  • KPSS test
  • Differencing techniques
  • Detrending methods
  • Seasonal adjustment
  • Transformation methods
5

ARIMA Models

Master AutoRegressive Integrated Moving Average models for time series forecasting.

  • AR, MA, and ARMA models
  • ARIMA model structure
  • Model identification
  • Parameter estimation
  • Box-Jenkins methodology
  • Information criteria
  • Diagnostic checking
  • Forecasting with ARIMA
6

Seasonal ARIMA Models

Extend ARIMA models to handle seasonal patterns in time series data.

  • Seasonal ARIMA (SARIMA)
  • Seasonal differencing
  • Seasonal parameters
  • Model notation
  • Seasonal diagnostics
  • Multiple seasonality
  • Airline model
  • Seasonal forecasting
7

Exponential Smoothing

Learn exponential smoothing methods for forecasting and trend analysis.

  • Simple exponential smoothing
  • Double exponential smoothing
  • Triple exponential smoothing
  • Holt-Winters method
  • State space models
  • ETS framework
  • Parameter optimization
  • Confidence intervals
8

Advanced Time Series Models

Explore advanced modeling techniques including GARCH, VAR, and state space models.

  • GARCH models for volatility
  • Vector Autoregression (VAR)
  • Cointegration analysis
  • Error correction models
  • State space models
  • Kalman filtering
  • Regime switching models
  • Threshold models
9

Machine Learning for Time Series

Apply machine learning techniques to time series forecasting and analysis.

  • Feature engineering for time series
  • Lag features and windows
  • Random Forest for forecasting
  • XGBoost time series
  • LSTM neural networks
  • Prophet model
  • Ensemble methods
  • Cross-validation strategies
10

Multivariate Time Series

Analyze multiple time series simultaneously and model their interactions.

  • Multivariate analysis concepts
  • Cross-correlation analysis
  • Vector Autoregression (VAR)
  • Granger causality
  • Impulse response functions
  • Forecast error variance
  • Structural VAR models
  • Panel data analysis
11

Model Evaluation and Selection

Learn methods to evaluate forecast accuracy and select optimal time series models.

  • Forecast accuracy metrics
  • Mean Absolute Error (MAE)
  • Root Mean Square Error (RMSE)
  • Mean Absolute Percentage Error
  • Symmetric MAPE
  • Information criteria
  • Cross-validation for time series
  • Model comparison techniques
12

Applied Time Series Projects

Apply time series analysis to real-world problems across different domains.

  • Financial time series analysis
  • Economic forecasting
  • Demand forecasting
  • Energy consumption prediction
  • Weather data analysis
  • Web traffic forecasting
  • IoT sensor data
  • Production and deployment

Unit 1: Time Series Fundamentals

Understand the basic concepts of time series data and its unique characteristics.

What is Time Series Data

Learn the fundamental definition of time series as data points collected sequentially over time.

Sequential Temporal Ordered
Time series data consists of observations recorded at successive points in time, where the temporal order is crucial for analysis and the time intervals are typically uniform.

Temporal Dependence

Understand how current values in time series depend on previous observations.

import pandas as pd
import numpy as np

# Create time series with temporal dependence
dates = pd.date_range('2020-01-01', periods=100, freq='D')
# AR(1) process: y_t = 0.5 * y_{t-1} + noise
y = [10] # Initial value
for i in range(1, 100):
  y.append(0.5 * y[i-1] + np.random.normal(0, 1))

ts = pd.Series(y, index=dates)
print(f"Autocorrelation at lag 1: {ts.autocorr(lag=1):.3f}")

Types of Time Series

Classify time series based on different characteristics and measurement scales.

Continuous vs Discrete: Based on measurement scale
Univariate vs Multivariate: Number of variables
Regular vs Irregular: Time interval consistency
# Examples of different time series types
import matplotlib.pyplot as plt

# Continuous: Stock prices
stock_prices = pd.Series([100, 102.5, 101.8, 103.2])

# Discrete: Daily sales count
daily_sales = pd.Series([25, 30, 28, 35])

# Irregular: Event timestamps
events = pd.Series([1, 1, 0, 1],
  index=pd.to_datetime(['2023-01-01', '2023-01-03',
                        '2023-01-08', '2023-01-10']))

Time Series Components

Learn about the fundamental components that make up time series: trend, seasonality, and noise.

Trend Seasonality Cyclical Irregular
Additive Model: Y(t) = Trend(t) + Seasonal(t) + Irregular(t)
Multiplicative Model: Y(t) = Trend(t) × Seasonal(t) × Irregular(t)
from statsmodels.tsa.seasonal import seasonal_decompose

# Decompose time series
decomposition = seasonal_decompose(ts, model='additive', period=12)

# Extract components
trend = decomposition.trend
seasonal = decomposition.seasonal
residual = decomposition.resid

# Plot components
fig, axes = plt.subplots(4, 1, figsize=(12, 10))
ts.plot(ax=axes[0], title='Original')
trend.plot(ax=axes[1], title='Trend')
seasonal.plot(ax=axes[2], title='Seasonal')
residual.plot(ax=axes[3], title='Residual')

Stationarity Concepts

Understand the crucial concept of stationarity and its importance in time series analysis.

Stationary series: Statistical properties (mean, variance, covariance) remain constant over time
Non-stationary: Properties change over time (trending, changing variance)
from statsmodels.tsa.stattools import adfuller

# Test for stationarity
def check_stationarity(timeseries):
  # Augmented Dickey-Fuller test
  result = adfuller(timeseries.dropna())
  
  print(f'ADF Statistic: {result[0]:.4f}')
  print(f'p-value: {result[1]:.4f}')
  
  if result[1] <= 0.05:
    print("Series is stationary")
  else:
    print("Series is non-stationary")

check_stationarity(ts)

Seasonality Patterns

Identify and understand different types of seasonal patterns in time series data.

# Generate seasonal time series
t = np.arange(1, 49) # 4 years of monthly data
trend = 0.5 * t
seasonal = 10 * np.sin(2 * np.pi * t / 12) # Annual seasonality
noise = np.random.normal(0, 2, len(t))

ts_seasonal = trend + seasonal + noise

# Plot seasonal pattern
plt.figure(figsize=(12, 6))
plt.plot(ts_seasonal, label='Time Series')
plt.plot(trend, label='Trend', linestyle='--')
plt.plot(seasonal, label='Seasonal', linestyle=':')
plt.legend()
plt.title('Time Series with Trend and Seasonality')