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  2. Technical Notes

Technical Notes

We originally composed these technical notes after sitting in on a time series analysis class. Over the years, we have maintained these notes and added new insights, empirical observations and intuitions acquired. We often go back to these notes for resolving development issues and/or to properly address a product support matter.

Data Preparation

  • Stationarity
  • Homogeneity
  • Concentration of Values
  • Outliers
  • Missing Values

Descriptive Statistics

  • KDE Optimization – Unbiased Cross-Validation
  • KDE – Direct Plug-In Method
  • KDE Optimization Primer
  • A Correlogram tale
  • The Ins and Outs of Histograms
  • Which autocorrelation (ACF) estimation method should I use?

Statistical Testing

  • Augmented Dickey-Fuller Test
  • ARCH Test Explained

Smoothing

  • Part I - Different Smoothing Methods
  • Part II - Auto-Calibrate Values of Smoothing Parameters
  • Part III - Finding Optimal Initial Values for Smoothing
  • Keep up with the trends

Forecasting Performance

  • Forecast Performance Measures Survey

Modeling

  • Calendar Effects
  • Patterns Unplugged
  • For goodness of fit's sake
  • Backward Forecast

ARMA/ARIMA Modeling

  • Moving Average (MA) Model
  • Autoregressive (AR) Model
  • ARMA Unplugged
  • ARIMA to the Rescue
  • X12-ARIMA Support with NumXL

ARCH/GARCH Modeling

  • Understanding Exponential Weighted Volatility (EWMA)
  • Volatility 1: The Basics
  • Volatility 2: Future Volatility Modeling
  • Volatility 3: Autoregressive Conditional Heteroscedasticity (ARCH)

Factors Analysis

  • Multiple Linear Regression (MLR) Forecast Error

Spectral Analysis

  • Calculating Signal-to-Noise Ratio Using DFT
  • Discrete Fourier Transform (DFT) - Trigonometric Representation
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