hi

thanks for putting this package together - this is indeed an incredible package. what are your thoughts on using Apple Accelerate? I feel it might help those of us on Macs?

https://github.com/JuliaLinearAlgebra/AppleAccelerate.jl

thanks
Roh

I deal with recorded data with a sampling speed above 99kHz, if a signal comprises ten periods @0.1Hz the number of points is quite huge (these big data files is the reason for Julia instead of Octave).
Now my idea was, to utilize the esprit-function to calculate the initial guess for the frequencies in a signal, unfortunately Julia v1.6.7 throws the error message above, you can reproduce this error if you generate a signal with e.g. 19999901 points :-(

I'm new to ssa. But the book I read suggests ssa makes the assumption of a linear recurrent relationship (lrr), which can be used for forecasting.

What is the relationship of current implementation of prediction, say fit_trend, with lrr?
Or is it a different approach that was implemented here?

Thanks!

reference: https://en.wikipedia.org/wiki/Singular_spectrum_analysis#Forecasting_by_SSA

Does your SingularSpectrumAnalysis also cover Multivariate/multichannel SSA as in https://arxiv.org/pdf/1309.5050 ?

I see that you follow DifferentialEquations.jl and other items in nonlinear dynamics. You may be interested to see JuliaDynamics where there is an implementation of Bloomhead and King (SSA) in nlts.jl applied to the gissinger model.

@JuliaRegistrator register()

Hello, thanks for the great work on this package!
I am working with complex valued time series and I noticed that using the analyse function with a complex-valued signal yields an "Inexact" error which comes from the reconstruct function. I think a simple way to make the method adapted to both real and complex valued signals would be to replace the line 101 of your code in the reconstruct function:

" yr = zeros(N,M)"
could be changed for
" yr = Array{Complex{Float64}}(undef,N,M)"

Cheers,
Jeanne.

This package cannot deal with time series with missing data, would that be the future plan?
Also, SSA is an important methods in gap filling and data forecasting. will this be in future plan?

As I know, there is a such package in R, which is very powerful yet the speed is not as fast as this package in Julia.

Thanks!

Hi,
1.)
if I specify that two frequencies should be calculated (field "f"), it returns three.
2.)
Two frequencies are embedded but only one is calculated correctly

Attached my sample code:

using Printf, RobustModels
using DSP, SingularSpectrumAnalysis # both provide implementations of esprit()
# using MLJ # provides rms()

## --- compose signals: clean and disturbed --------------------------------------------------------------------------------
sampling_rate   = 10000                    # Sampling frequency
n_signal        = 3000                     # Length of signal
off_set_sign    = 1.0                      # vertical offset of signal
frequ_A         = 50.0                     # unit = Hz
frequ_B         = 120.0                    # unit = Hz
ampl_A          = 0.7                      # Amplitude @f1
ampl_B          = 1.0                      # Amplitude @f2
noise_ampl      = 0.3;                     # max noise amplitude
b_symmetry_on   = false                    # substract arithmetic mean before decomposition

# --- time vector: vec_t
delta_t         = 1.0 / sampling_rate     # Time step in sec
vec_t           = collect(range(0, step = delta_t, length = n_signal))  # Time vector

# create signal with sinus at frequ_A and frequ_B:
signal_clean     = off_set_sign .+ ampl_A .* sin.(2 * pi * frequ_A .* vec_t)  +  ampl_B .* sin.(2 * pi * frequ_B .* vec_t)
signal_disturbed = signal_clean + noise_ampl * randn(size(vec_t))
if b_symmetry_on
    signal_disturbed    = signal_disturbed .- mean(signal_disturbed)
    signal_clean        = signal_clean     .- mean(signal_clean)
end

## --- main ----------------------------------------------------------------------------------------------------------------
# --- check if values for amplitude higth are meaningful and figure out, if one or two amplitudes are larger then 0
if ampl_A > 0       &&  ampl_B == 0
    num_of_frequ = 1
elseif ampl_A == 0  &&  ampl_B > 0
    num_of_frequ = 1
elseif ampl_A > 0   &&  ampl_B > 0 
    num_of_frequ = 2
else
    error("Either amplitude A or B needs to be positive!")
end
# --- calculate frequency via function "esprit()"
# source esprit function A: https://docs.juliadsp.org/stable/estimation/
# source esprit function B: https://github.com/baggepinnen/SingularSpectrumAnalysis.jl/blob/master/src/SingularSpectrumAnalysis.jl#L158
# --- size of correlation matrix: equation is according to van der Veen and Leus: (n_signal + 1)/3.
lag_embedding_dimension = round(Int, (n_signal + 1)/3) # Size of lag embedding and the covariance matrix used (size of correlation matrix).
esprit_frequ_methode_A = DSP.Estimation.esprit(signal_clean, lag_embedding_dimension, 2*num_of_frequ, sampling_rate)
esprit_result = SingularSpectrumAnalysis.esprit(signal_clean, lag_embedding_dimension, num_of_frequ, fs = sampling_rate, robust = false)
esprit_frequ_methode_B = esprit_result.f
# ---
if size(esprit_frequ_methode_B)[1] > num_of_frequ
    error("Singal does not seem to be symetric around zero!")
end
# ---
if num_of_frequ == 2
    println(@sprintf("Frequency A: %.1f Hz, Frequ B: %.1f Hz, esprit result[1]: %.1f Hz, esprit_result[2]: %.1f Hz", 
    frequ_A, frequ_B, esprit_result.f[1], esprit_result.f[2] ))
end

When I change the ar_order argument in PredictionData(yt, ys, trend_order=1, ar_order=2) to anything more than 2, I get the following error (when using 6, for example):

ERROR: BoundsError: attempt to access 3-element Array{Float64,1} at index [7]

I’m not sure which 3-element Array it is trying to access, but it seems to always contain 3 elements, no matter what I do.

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hi

thanks for putting this together, great package. qq: do we know if there is a way SSA or this library can handle streaming data? I have a lot of streaming data and performance is quite key.

thanks
Roh

Great package.

I've upgraded to 1.9.0 and have noticed that the performance is now significantly slower compared to 1.7.3?

I'm using analyze(TimeSeries, n, robust=Robust).

Any particular reason for this?

Thanks.