 # How To Identify Patterns in Time Series Data: Time Series Analysis In the following topics, we will first review techniques used to identify patterns in time series data (such as smoothing and curve fitting techniques and autocorrelations), then we will introduce a general class of models that can be used to represent time series data and generate predictions (autoregressive and moving average models). Finally, we will review some simple but commonly used modeling and forecasting techniques based on linear regression. For more information see the topics below. General Introduction In the following topics, we will review techniques that are useful for analyzing time series data, that is, sequences of measurements that follow non-random orders. Unlike the analyses of random samples of observations that are discussed in the context of most other statistics, the analysis of time series is based on the assumption that successive values in the data file represent consecutive measurements taken at equally spaced time intervals. Two Main Goals Trend Analysis t -

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Assumptions of Statistical Tests “All models are incorrect. Some are useful.” George Box When you do a statistical test, you are, in essence, testing if the assumptions are valid. We are typically only interested in one, the null hypothesis. That is, the assumption that the difference is zero (actually it could test if the difference were any amount). Applied Time Series Analysis [Home] [Lectures] [Assignments] [Exams] Introduction Model-based forecasting methods; autoregressive and moving average models; ARIMA, ARMAX, ARCH, and state-space models; estimation, forecasting and model validation; missing data; irregularly spaced time series; parametric and nonparametric bootstrap methods for time series; multiresolution analysis of spatial and time-series signals; and time-varying models and wavelets.

Concepts for Fourier Transforms A signal can be viewed from two different standpoints: The frequency domain The time domain In astronomy the frequency domain is perhaps the most familiar, because a spectrometer, e.g. a prism or a diffraction grating, splits light into its component color or frequencies and permits us to record its spectral content. This is like the trace on a spectrum analyzer, where the horizontal deflection is the frequency variable and the vertical deflection is the signals amplitude at that frequency. Distributions in Mathematica These notes explain how to compute probabilities for common statistical distributions using Mathematica. See also notes on working with distributions in R and S-PLUS, Excel, and in Python with SciPy. Distribution objects

Introduction to ANOVA Introduction to ANOVA (Jump to: Lecture | Video ) An ANOVA has factors(variables), and each of those factors has levels: There are several different types of ANOVA: There are four main assumptions of an ANOVA: Hypotheses in ANOVA depend on the number of factors you're dealing with: R Programming Welcome to the R programming Wikibook This book is designed to be a practical guide to the R programming language. R is free software designed for statistical computing. There is already great documentation for the standard R packages on the Comprehensive R Archive Network (CRAN) and many resources in specialized books, forums such as Stackoverflow and personal blogs, but all of these resources are scattered and therefore difficult to find and to compare. The aim of this Wikibook is to be the place where anyone can share his or her knowledge and tricks on R.

Assessing Linear Models in R In this post I will look at several techniques for assessing linear models in R, via the IPython Notebook interface. I find the notebook interface to be more convenient for development and debugging because it allows one to evaluate cells instead of going back and forth between a script and a terminal. If you do not have the IPython Notebook, then you can check it out here. Chart of distribution relationships Probability distributions have a surprising number inter-connections. A dashed line in the chart below indicates an approximate (limit) relationship between two distribution families. A solid line indicates an exact relationship: special case, sum, or transformation. Click on a distribution for the parameterization of that distribution. Click on an arrow for details on the relationship represented by the arrow. Follow @ProbFact on Twitter to get one probability fact per day, such as the relationships on this diagram.

Problem of alpha inflation The main problem that designers of post hoc tests try to deal with is -inflation. This refers to the fact that the more tests you conduct at = .05, the more likely you are to claim you have a significant result when you shouldn't have (i.e., a Type I error). R Starter Kit R Starter Kit This page is intended for people who: These materials have been collected from various places on our website and have been ordered so that you can, in step-by-step fashion, develop the skills needed to conduct common analyses in R. Getting familiar with R Class notes: There is no point in waiting to take an introductory class on how to use R. Instead, we have notes of our introductory class that you can download and view. Visual Representation of SQL Joins Introduction This is just a simple article visually explaining SQL JOINs. Background I'm a pretty visual person. Things seem to make more sense as a picture.

Diagram of conjugate prior relationships The following diagram summarizes conjugate prior relationships for a number of common sampling distributions. Arrows point from a sampling distribution to its conjugate prior distribution. The symbol near the arrow indicates which parameter the prior is unknown. These relationships depends critically on choice of parameterization, some of which are uncommon. determine sample size two-way ANOVA? Computing required sample size for experiments to be analyzed by ANOVA is pretty complicated, with lots of possiblilities. To learn more, consult books by Cohen or Bausell and Li, but plan to spend at least several hours. Two-way ANOVA, as you'd expect, is more complicated than one-way. The complexity comes from the many possible ways to phrase your question about sample size.

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