def true_cov_ma1_of_t(t_par, sigma, lag):
"""
True autocovariance for given parameters.
:param t_par: t parameter of a scaled time.
:param sigma: standard deviation of noise used to simulate the MA1 sample.
:param lag: lag of autocovariance to be computed.
:return: true autocovariance value.
"""
if lag == 0:
return (sigma**2) * (1 + (coef(t_par=t_par)**2))
elif lag == 1:
return coef(t_par=t_par) * (sigma**2)
else:
return 0
def horizontal_sample_tvma1(sample_size: int,
t_par_count: int,
mean: int,
sigma: int,
noise_type: str,
noise=None):
"""
Generates MA(1) sample for the given noise or its parameters.
:sample_size: number of observations or number of columns in the returned matrix.
:t_par_count: number of t values or number of rows in the returned matrix.
:mean: mean of the noise.
:return: a double array t_par_count by sample_size
of stationary MA1 samples. Each line, corresponding to tPar value.
"""
if noise is None:
noise = create_noise(noise_size=sample_size + 1, mean=mean, sigma=sigma,
noise_type=noise_type)
elif len(noise) != sample_size + 1:
raise ValueError("length of noise should be sample_size + 1")
t_par_array = create_t_par_array(t_par_count=t_par_count)
horizontal_sample_tvma1 = np.full(shape=(t_par_count,sample_size),
fill_value=np.nan)
for i in range(t_par_count):
for j in range(sample_size):
horizontal_sample_tvma1[i, j] = coef(t_par=t_par_array[i]) * \
noise[j] + noise[j + 1]
return horizontal_sample_tvma1
def diagonal_sample_scaled_noise(sample_size: int,
mean: int,
sigma: int,
noise_type: str,
noise=None):
"""
Currently unused.
Copied from the first project with translation from R to Python.
Forms a diagonal sample of noise, stretched by coef(t) values
at each index point.
:sample_size: size of a sample to be generated.
:mean: mean of a notise to be genrated.
:noise_type: "gaussian" or "bernoulli".
:return: one-dimensional array of noise values.
"""
if noise is None:
noise = create_noise(noise_size=sample_size + 1,
mean=mean,
sigma=sigma,
noise_type=noise_type)
elif len(noise) != sample_size + 1:
raise ValueError("length of noise should be sample_size + 1")
diagonal_sample_scaled_noise = np.full(shape=sample_size,
fill_value=np.nan)
for i in range(1, sample_size + 1):
diagonal_sample_scaled_noise[i - 1] = coef(t_par=i / sample_size) * \
noise[i - 1]
return diagonal_sample_scaled_noise
def diagonal_sample_tvma3(sample_size: int,
mean: int,
sigma: int,
noise_type: str,
noise=None):
"""
Creates the diagonal time-varying MA3 sample, given
sample size, mean, sigma and noise type.
:param sample_size: size of a sample to be generated.
:param mean: mean of the noise to generate, if not given.
:param sigma: sigma of the noise to generate, if not given.
:param noise_type: type of the noise to generate, if not given.
:param noise: an array of the size sample_size+3. If it is given (not None), then sample size agreement is checked, and other arguments ignored.
The cycle starts from 1, not from 0, because
we pass i+1 to theta.
Basically, indexation in Python is x(0), ...x(n-1),
while in formulas, it is for the case x(1), ...x(n).
"""
if noise is None:
noise = create_noise(noise_size=sample_size + 3, mean=mean, sigma=sigma,
noise_type=noise_type)
elif len(noise) != sample_size + 3:
raise ValueError("length of noise should be sample_size + 3")
diagonal_sample_tvma3 = np.full(shape=sample_size, fill_value=np.nan)
for i in range(1, sample_size + 1):
diagonal_sample_tvma3[i - 1] = noise[i + 2] + \
coef(t_par=i / sample_size) * noise[i + 1] + \
coef_2(t_par=i / sample_size) * noise[i] + \
coef_3(t_par=i / sample_size) * noise[i - 1]
return diagonal_sample_tvma3
def horizontal_sample_scaled_noise(sample_size: int,
t_par_count: int,
mean: int,
sigma: int,
noise_type: str,
noise=None):
"""
Creates and returns a double array of dimensions [sample_size, t_par_count].
Each row is a noise sample, streched by coef(t).
So it produces the double array with proportional rows.
"""
if noise is None:
noise = create_noise(noise_size=sample_size + 1,
mean=mean,
sigma=sigma,
noise_type=noise_type)
elif len(noise) != sample_size + 1:
raise ValueError("length of noise should be sample_size + 1")
t_par_array = create_t_par_array(t_par_count=t_par_count)
horizontal_sample_tvma1 = np.full(shape=(t_par_count, sample_size),
fill_value=np.nan)
for i in range(t_par_count):
for j in range(sample_size):
horizontal_sample_tvma1[i, j] = coef(t_par=t_par_array[i]) * \
noise[j]
return horizontal_sample_tvma1
def diagonal_sample_tvma1(sample_size: int,
mean: float,
sigma: float,
noise_type: str,
noise=None) -> np.array:
"""
Create diagonal sample tvma1.
:param sample_size: len of sample
:param mean: mean
:param sigma: sigma
:param noise_type: type
:return: diagonal sample tvma1
"""
if noise is None:
noise = create_noise(noise_size=sample_size + 1,
mean=mean,
sigma=sigma,
noise_type=noise_type)
elif len(noise) != sample_size + 1:
raise ValueError("length of noise should be sample_size + 1")
diagonal_sample_tvma1 = np.full(shape=sample_size, fill_value=np.nan)
for i in range(1, sample_size + 1):
diagonal_sample_tvma1[
i - 1] = coef(t_par=i / sample_size) * noise[i - 1] + noise[i]
return diagonal_sample_tvma1
def true_lrv_ma3_of_single_t(sigma, t_par):
"""
True local LRV for given parameters.
:param sigma: standard deviation of noise used to simulate the MA3 sample.
:param t_par: t parameter or scaled time.
:return: true LRV value.
"""
lrv = (sigma**2) * (1 + coef(t_par) + coef_2(t_par) + coef_3(t_par))**2
return lrv
def true_cov_scaled_noise_of_t(t_par, sigma, lag):
"""
True autocovariance for given parameters.
:param t_par: t parameter of a scaled time.
:param sigma: standard deviation of noise used to simulate the scaled noise sample.
:param lag: lag of autocovariance to be computed.
:return: true autocovariance value.
"""
if lag == 0:
return coef(t_par=t_par)**2 * sigma**2
elif lag != 0:
return 0
def true_cov_ma3_of_t(t_par, lag, sigma):
"""
True autocovariance for given parameters.
:param t_par: t parameter of a scaled time.
:param sigma: standard deviation of noise used to simulate the MA3 sample.
:param lag: lag of autocovariance to be computed.
:return: true autocovariance value.
"""
if lag == 0:
return ((1**2) + (coef(t_par=t_par)**2) + (coef_2(t_par=t_par)**2) +
(coef_3(t_par=t_par)**2)) * (sigma**2)
elif lag == 1:
return (1 * coef(t_par=t_par) + coef(t_par=t_par) *
coef_2(t_par=t_par) + coef_2(t_par=t_par) * coef_3(t_par=t_par))\
* (sigma ** 2)
elif lag == 2:
return (1 * coef_2(t_par=t_par) +
coef(t_par=t_par) * coef_3(t_par=t_par)) * (sigma**2)
elif lag == 3:
return (1 * coef_3(t_par=t_par)) * (sigma**2)
else:
return 0