"""Linear Filters for time series analysis and testing TODO: * check common sequence in signature of filter functions (ar,ma,x) or (x,ar,ma) Created on Sat Oct 23 17:18:03 2010 Author: Josef-pktd """ # not original copied from various experimental scripts # version control history is there import numpy as np import scipy.fftpack as fft from scipy import signal try: from scipy.signal._signaltools import _centered as trim_centered except ImportError: # Must be using SciPy <1.8.0 where this function was moved (it's not a # public SciPy function, but we need it here) from scipy.signal.signaltools import _centered as trim_centered from statsmodels.tools.validation import array_like, PandasWrapper def _pad_nans(x, head=None, tail=None): if np.ndim(x) == 1: if head is None and tail is None: return x elif head and tail: return np.r_[[np.nan] * head, x, [np.nan] * tail] elif tail is None: return np.r_[[np.nan] * head, x] elif head is None: return np.r_[x, [np.nan] * tail] elif np.ndim(x) == 2: if head is None and tail is None: return x elif head and tail: return np.r_[[[np.nan] * x.shape[1]] * head, x, [[np.nan] * x.shape[1]] * tail] elif tail is None: return np.r_[[[np.nan] * x.shape[1]] * head, x] elif head is None: return np.r_[x, [[np.nan] * x.shape[1]] * tail] else: raise ValueError("Nan-padding for ndim > 2 not implemented") #original changes and examples in sandbox.tsa.try_var_convolve # do not do these imports, here just for copied fftconvolve #get rid of these imports #from scipy.fftpack import fft, ifft, ifftshift, fft2, ifft2, fftn, \ # ifftn, fftfreq #from numpy import product,array # previous location in sandbox.tsa.try_var_convolve def fftconvolveinv(in1, in2, mode="full"): """ Convolve two N-dimensional arrays using FFT. See convolve. copied from scipy.signal.signaltools, but here used to try out inverse filter. does not work or I cannot get it to work 2010-10-23: looks ok to me for 1d, from results below with padded data array (fftp) but it does not work for multidimensional inverse filter (fftn) original signal.fftconvolve also uses fftn """ s1 = np.array(in1.shape) s2 = np.array(in2.shape) complex_result = (np.issubdtype(in1.dtype, np.complex) or np.issubdtype(in2.dtype, np.complex)) size = s1+s2-1 # Always use 2**n-sized FFT fsize = 2**np.ceil(np.log2(size)) IN1 = fft.fftn(in1,fsize) #IN1 *= fftn(in2,fsize) #JP: this looks like the only change I made IN1 /= fft.fftn(in2,fsize) # use inverse filter # note the inverse is elementwise not matrix inverse # is this correct, NO does not seem to work for VARMA fslice = tuple([slice(0, int(sz)) for sz in size]) ret = fft.ifftn(IN1)[fslice].copy() del IN1 if not complex_result: ret = ret.real if mode == "full": return ret elif mode == "same": if np.product(s1,axis=0) > np.product(s2,axis=0): osize = s1 else: osize = s2 return trim_centered(ret,osize) elif mode == "valid": return trim_centered(ret,abs(s2-s1)+1) #code duplication with fftconvolveinv def fftconvolve3(in1, in2=None, in3=None, mode="full"): """ Convolve two N-dimensional arrays using FFT. See convolve. For use with arma (old version: in1=num in2=den in3=data * better for consistency with other functions in1=data in2=num in3=den * note in2 and in3 need to have consistent dimension/shape since I'm using max of in2, in3 shapes and not the sum copied from scipy.signal.signaltools, but here used to try out inverse filter does not work or I cannot get it to work 2010-10-23 looks ok to me for 1d, from results below with padded data array (fftp) but it does not work for multidimensional inverse filter (fftn) original signal.fftconvolve also uses fftn """ if (in2 is None) and (in3 is None): raise ValueError('at least one of in2 and in3 needs to be given') s1 = np.array(in1.shape) if in2 is not None: s2 = np.array(in2.shape) else: s2 = 0 if in3 is not None: s3 = np.array(in3.shape) s2 = max(s2, s3) # try this looks reasonable for ARMA #s2 = s3 complex_result = (np.issubdtype(in1.dtype, np.complex) or np.issubdtype(in2.dtype, np.complex)) size = s1+s2-1 # Always use 2**n-sized FFT fsize = 2**np.ceil(np.log2(size)) #convolve shorter ones first, not sure if it matters IN1 = in1.copy() # TODO: Is this correct? if in2 is not None: IN1 = fft.fftn(in2, fsize) if in3 is not None: IN1 /= fft.fftn(in3, fsize) # use inverse filter # note the inverse is elementwise not matrix inverse # is this correct, NO does not seem to work for VARMA IN1 *= fft.fftn(in1, fsize) fslice = tuple([slice(0, int(sz)) for sz in size]) ret = fft.ifftn(IN1)[fslice].copy() del IN1 if not complex_result: ret = ret.real if mode == "full": return ret elif mode == "same": if np.product(s1,axis=0) > np.product(s2,axis=0): osize = s1 else: osize = s2 return trim_centered(ret,osize) elif mode == "valid": return trim_centered(ret,abs(s2-s1)+1) #original changes and examples in sandbox.tsa.try_var_convolve #examples and tests are there def recursive_filter(x, ar_coeff, init=None): """ Autoregressive, or recursive, filtering. Parameters ---------- x : array_like Time-series data. Should be 1d or n x 1. ar_coeff : array_like AR coefficients in reverse time order. See Notes for details. init : array_like Initial values of the time-series prior to the first value of y. The default is zero. Returns ------- array_like Filtered array, number of columns determined by x and ar_coeff. If x is a pandas object than a Series is returned. Notes ----- Computes the recursive filter :: y[n] = ar_coeff[0] * y[n-1] + ... + ar_coeff[n_coeff - 1] * y[n - n_coeff] + x[n] where n_coeff = len(n_coeff). """ pw = PandasWrapper(x) x = array_like(x, 'x') ar_coeff = array_like(ar_coeff, 'ar_coeff') if init is not None: # integer init are treated differently in lfiltic init = array_like(init, 'init') if len(init) != len(ar_coeff): raise ValueError("ar_coeff must be the same length as init") if init is not None: zi = signal.lfiltic([1], np.r_[1, -ar_coeff], init, x) else: zi = None y = signal.lfilter([1.], np.r_[1, -ar_coeff], x, zi=zi) if init is not None: result = y[0] else: result = y return pw.wrap(result) def convolution_filter(x, filt, nsides=2): """ Linear filtering via convolution. Centered and backward displaced moving weighted average. Parameters ---------- x : array_like data array, 1d or 2d, if 2d then observations in rows filt : array_like Linear filter coefficients in reverse time-order. Should have the same number of dimensions as x though if 1d and ``x`` is 2d will be coerced to 2d. nsides : int, optional If 2, a centered moving average is computed using the filter coefficients. If 1, the filter coefficients are for past values only. Both methods use scipy.signal.convolve. Returns ------- y : ndarray, 2d Filtered array, number of columns determined by x and filt. If a pandas object is given, a pandas object is returned. The index of the return is the exact same as the time period in ``x`` Notes ----- In nsides == 1, x is filtered :: y[n] = filt[0]*x[n-1] + ... + filt[n_filt-1]*x[n-n_filt] where n_filt is len(filt). If nsides == 2, x is filtered around lag 0 :: y[n] = filt[0]*x[n - n_filt/2] + ... + filt[n_filt / 2] * x[n] + ... + x[n + n_filt/2] where n_filt is len(filt). If n_filt is even, then more of the filter is forward in time than backward. If filt is 1d or (nlags,1) one lag polynomial is applied to all variables (columns of x). If filt is 2d, (nlags, nvars) each series is independently filtered with its own lag polynomial, uses loop over nvar. This is different than the usual 2d vs 2d convolution. Filtering is done with scipy.signal.convolve, so it will be reasonably fast for medium sized data. For large data fft convolution would be faster. """ # for nsides shift the index instead of using 0 for 0 lag this # allows correct handling of NaNs if nsides == 1: trim_head = len(filt) - 1 trim_tail = None elif nsides == 2: trim_head = int(np.ceil(len(filt)/2.) - 1) or None trim_tail = int(np.ceil(len(filt)/2.) - len(filt) % 2) or None else: # pragma : no cover raise ValueError("nsides must be 1 or 2") pw = PandasWrapper(x) x = array_like(x, 'x', maxdim=2) filt = array_like(filt, 'filt', ndim=x.ndim) if filt.ndim == 1 or min(filt.shape) == 1: result = signal.convolve(x, filt, mode='valid') else: # filt.ndim == 2 nlags = filt.shape[0] nvar = x.shape[1] result = np.zeros((x.shape[0] - nlags + 1, nvar)) if nsides == 2: for i in range(nvar): # could also use np.convolve, but easier for swiching to fft result[:, i] = signal.convolve(x[:, i], filt[:, i], mode='valid') elif nsides == 1: for i in range(nvar): result[:, i] = signal.convolve(x[:, i], np.r_[0, filt[:, i]], mode='valid') result = _pad_nans(result, trim_head, trim_tail) return pw.wrap(result) # previously located in sandbox.tsa.garch def miso_lfilter(ar, ma, x, useic=False): """ Filter multiple time series into a single time series. Uses a convolution to merge inputs, and then lfilter to produce output. Parameters ---------- ar : array_like The coefficients of autoregressive lag polynomial including lag zero, ar(L) in the expression ar(L)y_t. ma : array_like, same ndim as x, currently 2d The coefficient of the moving average lag polynomial, ma(L) in ma(L)x_t. x : array_like The 2-d input data series, time in rows, variables in columns. useic : bool Flag indicating whether to use initial conditions. Returns ------- y : ndarray The filtered output series. inp : ndarray, 1d The combined input series. Notes ----- currently for 2d inputs only, no choice of axis Use of signal.lfilter requires that ar lag polynomial contains floating point numbers does not cut off invalid starting and final values miso_lfilter find array y such that: ar(L)y_t = ma(L)x_t with shapes y (nobs,), x (nobs, nvars), ar (narlags,), and ma (narlags, nvars). """ ma = array_like(ma, 'ma') ar = array_like(ar, 'ar') inp = signal.correlate(x, ma[::-1, :])[:, (x.shape[1] + 1) // 2] # for testing 2d equivalence between convolve and correlate # inp2 = signal.convolve(x, ma[:,::-1])[:, (x.shape[1]+1)//2] # np.testing.assert_almost_equal(inp2, inp) nobs = x.shape[0] # cut of extra values at end # TODO: initialize also x for correlate if useic: return signal.lfilter([1], ar, inp, zi=signal.lfiltic(np.array([1., 0.]), ar, useic))[0][:nobs], inp[:nobs] else: return signal.lfilter([1], ar, inp)[:nobs], inp[:nobs]