Spectral analysis

Spectral analysis is part of:

  • Time Time series analysis software

  • System configuration

    • Windows:
      • Versions: 9x/Me/NT/2000/XP/Vista/Win 7/Win 8
      • Excel: 97 and later
      • Processor: 32 or 64 bits
      • Hard disk: 150 Mb
    • Mac OS X:
      • OS: OS X
      • Excel: X, 2004 and 2011
      • Hard disk: 150Mb.

Benefits

  • Easy and user-friendly
    Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
  • Data and results shared seamlessly
    Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
  • Modular
    Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
  • Didactic
    Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
  • Affordable
    Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
  • Accessible - Available in many languages
    Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
  • Automatable and customizable
    Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.

Spectral analysis

Spectral analysis allows transforming a time series into its coordinates in the space of frequencies, and then to analyze its characteristics in this space. The magnitude and phase can be extracted from the coordinates. It is then possible to build representations such as the periodogram or the spectral density, and to test if the series is stationary. By studying the spectral density, seasonal components and/or noise can be identified. Spectral analysis is a very general method used in a variety of domains.

The spectral representation of a time series Xt, (t=1,…,n), decomposes Xt into a sum of sinusoidal components with uncorrelated random coefficients. From there we can obtain decomposition the autocovariance and autocorrelation functions into sinusoids.

Spectral density

The spectral density corresponds to the transform of a continuous time series. However, we usually have only access to a limited number of equally spaced data, and therefore, we need to obtain first the discrete Fourier coordinates (cosine and sine transforms), and then the periodogram. From the periodogram, using a smoothing function, we can obtain a spectral density estimate which is a better estimator of the spectrum.

The spectral density estimate (or discrete spectral average estimator) of the time series Xt uses weights. The weights, are either fixed by the user, or determined by the choice of a kernel. XLSTAT suggests the use of the following kernels:

White noise tests

XLSTAT optionally displays two test statistics and the corresponding p-values for white noise: Fisher's Kappa and Bartlett's Kolmogorov-Smirnov statistic.

XLSTAT-Time spectral analysis

Using fast and powerful methods, XLSTAT automatically computes the Fourier cosine and sine transforms of Xt, for each Fourier frequency, and then the various functions that derive from these transforms.

Tutorials

Screenshots