import numpy as np
from typing import Optional
import torch
import torch.nn as nn
import torch.nn.functional as F
from neuralforecast.common._modules import DataEmbedding
from neuralforecast.common._modules import SeriesDecomp
from neuralforecast.common._base_windows import BaseWindows
from neuralforecast.losses.pytorch import MAEFEDformer
FEDformer模型旨在解决在长时间预测中寻找可靠依赖关系的挑战，特别是在复杂的时间模式上。
该架构具有以下独特特征： - 基于移动平均滤波器的趋势和季节性分量的内置渐进分解。 - 频率增强块和频率增强注意力，以便在稀疏表示上执行注意力，例如傅里叶变换。 - Vaswani等人（2017）提出的经典编码器-解码器，结合多头注意力机制。
FEDformer模型利用三组分的方法来定义其嵌入： - 它采用从卷积网络获得的编码自回归特征。 - 利用从日历特征获得的绝对位置嵌入。
1. 辅助函数
class LayerNorm(nn.Module):
"""
专门为季节性部分设计的层归一化
"""
def __init__(self, channels):
super(LayerNorm, self).__init__()
self.layernorm = nn.LayerNorm(channels)
def forward(self, x):
x_hat = self.layernorm(x)
bias = torch.mean(x_hat, dim=1).unsqueeze(1).repeat(1, x.shape[1], 1)
return x_hat - bias
class AutoCorrelationLayer(nn.Module):
"""
自相关层
"""
def __init__(self, correlation, hidden_size, n_head, d_keys=None,
d_values=None):
super(AutoCorrelationLayer, self).__init__()
d_keys = d_keys or (hidden_size // n_head)
d_values = d_values or (hidden_size // n_head)
self.inner_correlation = correlation
self.query_projection = nn.Linear(hidden_size, d_keys * n_head)
self.key_projection = nn.Linear(hidden_size, d_keys * n_head)
self.value_projection = nn.Linear(hidden_size, d_values * n_head)
self.out_projection = nn.Linear(d_values * n_head, hidden_size)
self.n_head = n_head
def forward(self, queries, keys, values, attn_mask):
B, L, _ = queries.shape
_, S, _ = keys.shape
H = self.n_head
queries = self.query_projection(queries).view(B, L, H, -1)
keys = self.key_projection(keys).view(B, S, H, -1)
values = self.value_projection(values).view(B, S, H, -1)
out, attn = self.inner_correlation(
queries,
keys,
values,
attn_mask
)
out = out.view(B, L, -1)
return self.out_projection(out), attnclass EncoderLayer(nn.Module):
"""
具有渐进分解架构的FEDformer编码器层
"""
def __init__(self, attention, hidden_size, conv_hidden_size=None, MovingAvg=25, dropout=0.1, activation="relu"):
super(EncoderLayer, self).__init__()
conv_hidden_size = conv_hidden_size or 4 * hidden_size
self.attention = attention
self.conv1 = nn.Conv1d(in_channels=hidden_size, out_channels=conv_hidden_size, kernel_size=1, bias=False)
self.conv2 = nn.Conv1d(in_channels=conv_hidden_size, out_channels=hidden_size, kernel_size=1, bias=False)
self.decomp1 = SeriesDecomp(MovingAvg)
self.decomp2 = SeriesDecomp(MovingAvg)
self.dropout = nn.Dropout(dropout)
self.activation = F.relu if activation == "relu" else F.gelu
def forward(self, x, attn_mask=None):
new_x, attn = self.attention(
x, x, x,
attn_mask=attn_mask
)
x = x + self.dropout(new_x)
x, _ = self.decomp1(x)
y = x
y = self.dropout(self.activation(self.conv1(y.transpose(-1, 1))))
y = self.dropout(self.conv2(y).transpose(-1, 1))
res, _ = self.decomp2(x + y)
return res, attn
class Encoder(nn.Module):
"""
FEDformer编码器
"""
def __init__(self, attn_layers, conv_layers=None, norm_layer=None):
super(Encoder, self).__init__()
self.attn_layers = nn.ModuleList(attn_layers)
self.conv_layers = nn.ModuleList(conv_layers) if conv_layers is not None else None
self.norm = norm_layer
def forward(self, x, attn_mask=None):
attns = []
if self.conv_layers is not None:
for attn_layer, conv_layer in zip(self.attn_layers, self.conv_layers):
x, attn = attn_layer(x, attn_mask=attn_mask)
x = conv_layer(x)
attns.append(attn)
x, attn = self.attn_layers[-1](x)
attns.append(attn)
else:
for attn_layer in self.attn_layers:
x, attn = attn_layer(x, attn_mask=attn_mask)
attns.append(attn)
if self.norm is not None:
x = self.norm(x)
return x, attns
class DecoderLayer(nn.Module):
"""
具有渐进分解架构的FEDformer解码器层
"""
def __init__(self, self_attention, cross_attention, hidden_size, c_out, conv_hidden_size=None,
MovingAvg=25, dropout=0.1, activation="relu"):
super(DecoderLayer, self).__init__()
conv_hidden_size = conv_hidden_size or 4 * hidden_size
self.self_attention = self_attention
self.cross_attention = cross_attention
self.conv1 = nn.Conv1d(in_channels=hidden_size, out_channels=conv_hidden_size, kernel_size=1, bias=False)
self.conv2 = nn.Conv1d(in_channels=conv_hidden_size, out_channels=hidden_size, kernel_size=1, bias=False)
self.decomp1 = SeriesDecomp(MovingAvg)
self.decomp2 = SeriesDecomp(MovingAvg)
self.decomp3 = SeriesDecomp(MovingAvg)
self.dropout = nn.Dropout(dropout)
self.projection = nn.Conv1d(in_channels=hidden_size, out_channels=c_out, kernel_size=3, stride=1, padding=1,
padding_mode='circular', bias=False)
self.activation = F.relu if activation == "relu" else F.gelu
def forward(self, x, cross, x_mask=None, cross_mask=None):
x = x + self.dropout(self.self_attention(
x, x, x,
attn_mask=x_mask
)[0])
x, trend1 = self.decomp1(x)
x = x + self.dropout(self.cross_attention(
x, cross, cross,
attn_mask=cross_mask
)[0])
x, trend2 = self.decomp2(x)
y = x
y = self.dropout(self.activation(self.conv1(y.transpose(-1, 1))))
y = self.dropout(self.conv2(y).transpose(-1, 1))
x, trend3 = self.decomp3(x + y)
residual_trend = trend1 + trend2 + trend3
residual_trend = self.projection(residual_trend.permute(0, 2, 1)).transpose(1, 2)
return x, residual_trend
class Decoder(nn.Module):
"""
FEDformer解码器
"""
def __init__(self, layers, norm_layer=None, projection=None):
super(Decoder, self).__init__()
self.layers = nn.ModuleList(layers)
self.norm = norm_layer
self.projection = projection
def forward(self, x, cross, x_mask=None, cross_mask=None, trend=None):
for layer in self.layers:
x, residual_trend = layer(x, cross, x_mask=x_mask, cross_mask=cross_mask)
trend = trend + residual_trend
if self.norm is not None:
x = self.norm(x)
if self.projection is not None:
x = self.projection(x)
return x, trenddef get_frequency_modes(seq_len, modes=64, mode_select_method='random'):
"""
获取频域模式：
'random' 用于随机采样
'else' 用于采样最低模式；
"""
modes = min(modes, seq_len//2)
if mode_select_method == 'random':
index = list(range(0, seq_len // 2))
np.random.shuffle(index)
index = index[:modes]
else:
index = list(range(0, modes))
index.sort()
return index
class FourierBlock(nn.Module):
"""
傅里叶块
"""
def __init__(self, in_channels, out_channels, seq_len, modes=0, mode_select_method='random'):
super(FourierBlock, self).__init__()
# 获取频域模式
self.index = get_frequency_modes(seq_len, modes=modes, mode_select_method=mode_select_method)
self.scale = (1 / (in_channels * out_channels))
self.weights1 = nn.Parameter(
self.scale * torch.rand(8, in_channels // 8, out_channels // 8, len(self.index), dtype=torch.cfloat))
# 复乘法
def compl_mul1d(self, input, weights):
# (批次, 输入通道, x), (输入通道, 输出通道, x) -> (批次, 输出通道, x)
return torch.einsum("bhi,hio->bho", input, weights)
def forward(self, q, k, v, mask):
# 尺寸 = [批次大小, 长度, 隐藏层大小, 嵌入维度]
B, L, H, E = q.shape
x = q.permute(0, 2, 3, 1)
# 计算傅里叶系数
x_ft = torch.fft.rfft(x, dim=-1)
# 执行傅里叶神经操作
out_ft = torch.zeros(B, H, E, L // 2 + 1, device=x.device, dtype=torch.cfloat)
for wi, i in enumerate(self.index):
out_ft[:, :, :, wi] = self.compl_mul1d(x_ft[:, :, :, i], self.weights1[:, :, :, wi])
# 返回时域
x = torch.fft.irfft(out_ft, n=x.size(-1))
return (x, None)
class FourierCrossAttention(nn.Module):
"""
傅里叶交叉注意力层
"""
def __init__(self, in_channels, out_channels, seq_len_q, seq_len_kv, modes=64, mode_select_method='random',
activation='tanh', policy=0):
super(FourierCrossAttention, self).__init__()
self.activation = activation
self.in_channels = in_channels
self.out_channels = out_channels
# 在频域中获取查询和键（及值）的模式
self.index_q = get_frequency_modes(seq_len_q, modes=modes, mode_select_method=mode_select_method)
self.index_kv = get_frequency_modes(seq_len_kv, modes=modes, mode_select_method=mode_select_method)
self.scale = (1 / (in_channels * out_channels))
self.weights1 = nn.Parameter(
self.scale * torch.rand(8, in_channels // 8, out_channels // 8, len(self.index_q), dtype=torch.cfloat))
# 复乘法
def compl_mul1d(self, input, weights):
# (批次, 输入通道, x), (输入通道, 输出通道, x) -> (批次, 输出通道, x)
return torch.einsum("bhi,hio->bho", input, weights)
def forward(self, q, k, v, mask):
# 尺寸 = [批次大小, 长度, 隐藏层大小, 嵌入维度]
B, L, H, E = q.shape
xq = q.permute(0, 2, 3, 1) # 尺寸 = [批次大小, 头数, 嵌入维度, 层数]
xk = k.permute(0, 2, 3, 1)
#xv = v.permute(0, 2, 3, 1)
# 计算傅里叶系数
xq_ft_ = torch.zeros(B, H, E, len(self.index_q), device=xq.device, dtype=torch.cfloat)
xq_ft = torch.fft.rfft(xq, dim=-1)
for i, j in enumerate(self.index_q):
xq_ft_[:, :, :, i] = xq_ft[:, :, :, j]
xk_ft_ = torch.zeros(B, H, E, len(self.index_kv), device=xq.device, dtype=torch.cfloat)
xk_ft = torch.fft.rfft(xk, dim=-1)
for i, j in enumerate(self.index_kv):
xk_ft_[:, :, :, i] = xk_ft[:, :, :, j]
# 频域注意力机制
xqk_ft = (torch.einsum("bhex,bhey->bhxy", xq_ft_, xk_ft_))
if self.activation == 'tanh':
xqk_ft = xqk_ft.tanh()
elif self.activation == 'softmax':
xqk_ft = torch.softmax(abs(xqk_ft), dim=-1)
xqk_ft = torch.complex(xqk_ft, torch.zeros_like(xqk_ft))
else:
raise Exception('{} actiation function is not implemented'.format(self.activation))
xqkv_ft = torch.einsum("bhxy,bhey->bhex", xqk_ft, xk_ft_)
xqkvw = torch.einsum("bhex,heox->bhox", xqkv_ft, self.weights1)
out_ft = torch.zeros(B, H, E, L // 2 + 1, device=xq.device, dtype=torch.cfloat)
for i, j in enumerate(self.index_q):
out_ft[:, :, :, j] = xqkvw[:, :, :, i]
# 返回时域
out = torch.fft.irfft(out_ft / self.in_channels / self.out_channels, n=xq.size(-1))
return (out, None)2. 模型
class FEDformer(BaseWindows):
""" FEDformer
The FEDformer model tackles the challenge of finding reliable dependencies on intricate temporal patterns of long-horizon forecasting.
The architecture has the following distinctive features:
- In-built progressive decomposition in trend and seasonal components based on a moving average filter.
- Frequency Enhanced Block and Frequency Enhanced Attention to perform attention in the sparse representation on basis such as Fourier transform.
- Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.
The FEDformer model utilizes a three-component approach to define its embedding:
- It employs encoded autoregressive features obtained from a convolution network.
- Absolute positional embeddings obtained from calendar features are utilized.
*Parameters:*<br>
`h`: int, forecast horizon.<br>
`input_size`: int, maximum sequence length for truncated train backpropagation. Default -1 uses all history.<br>
`futr_exog_list`: str list, future exogenous columns.<br>
`hist_exog_list`: str list, historic exogenous columns.<br>
`stat_exog_list`: str list, static exogenous columns.<br>
`decoder_input_size_multiplier`: float = 0.5, .<br>
`version`: str = 'Fourier', version of the model.<br>
`modes`: int = 64, number of modes for the Fourier block.<br>
`mode_select`: str = 'random', method to select the modes for the Fourier block.<br>
`hidden_size`: int=128, units of embeddings and encoders.<br>
`dropout`: float (0, 1), dropout throughout Autoformer architecture.<br>
`n_head`: int=8, controls number of multi-head's attention.<br>
`conv_hidden_size`: int=32, channels of the convolutional encoder.<br>
`activation`: str=`GELU`, activation from ['ReLU', 'Softplus', 'Tanh', 'SELU', 'LeakyReLU', 'PReLU', 'Sigmoid', 'GELU'].<br>
`encoder_layers`: int=2, number of layers for the TCN encoder.<br>
`decoder_layers`: int=1, number of layers for the MLP decoder.<br>
`MovingAvg_window`: int=25, window size for the moving average filter.<br>
`loss`: PyTorch module, instantiated train loss class from [losses collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br>
`valid_loss`: PyTorch module, instantiated validation loss class from [losses collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br>
`max_steps`: int=1000, maximum number of training steps.<br>
`learning_rate`: float=1e-3, Learning rate between (0, 1).<br>
`num_lr_decays`: int=-1, Number of learning rate decays, evenly distributed across max_steps.<br>
`early_stop_patience_steps`: int=-1, Number of validation iterations before early stopping.<br>
`val_check_steps`: int=100, Number of training steps between every validation loss check.<br>
`batch_size`: int=32, number of different series in each batch.<br>
`valid_batch_size`: int=None, number of different series in each validation and test batch, if None uses batch_size.<br>
`windows_batch_size`: int=1024, number of windows to sample in each training batch, default uses all.<br>
`inference_windows_batch_size`: int=1024, number of windows to sample in each inference batch.<br>
`start_padding_enabled`: bool=False, if True, the model will pad the time series with zeros at the beginning, by input size.<br>
`scaler_type`: str='robust', type of scaler for temporal inputs normalization see [temporal scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).<br>
`random_seed`: int=1, random_seed for pytorch initializer and numpy generators.<br>
`num_workers_loader`: int=os.cpu_count(), workers to be used by `TimeSeriesDataLoader`.<br>
`drop_last_loader`: bool=False, if True `TimeSeriesDataLoader` drops last non-full batch.<br>
`alias`: str, optional, Custom name of the model.<br>
`optimizer`: Subclass of 'torch.optim.Optimizer', optional, user specified optimizer instead of the default choice (Adam).<br>
`optimizer_kwargs`: dict, optional, list of parameters used by the user specified `optimizer`.<br>
`lr_scheduler`: Subclass of 'torch.optim.lr_scheduler.LRScheduler', optional, user specified lr_scheduler instead of the default choice (StepLR).<br>
`lr_scheduler_kwargs`: dict, optional, list of parameters used by the user specified `lr_scheduler`.<br>
`**trainer_kwargs`: int, keyword trainer arguments inherited from [PyTorch Lighning's trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).<br>
"""
# 类属性
SAMPLING_TYPE = 'windows'
EXOGENOUS_FUTR = True
EXOGENOUS_HIST = False
EXOGENOUS_STAT = False
def __init__(self,
h: int,
input_size: int,
stat_exog_list = None,
hist_exog_list = None,
futr_exog_list = None,
decoder_input_size_multiplier: float = 0.5,
version: str = 'Fourier',
modes: int = 64,
mode_select: str = 'random',
hidden_size: int = 128,
dropout: float = 0.05,
n_head: int = 8,
conv_hidden_size: int = 32,
activation: str = 'gelu',
encoder_layers: int = 2,
decoder_layers: int = 1,
MovingAvg_window: int = 25,
loss = MAE(),
valid_loss = None,
max_steps: int = 5000,
learning_rate: float = 1e-4,
num_lr_decays: int = -1,
early_stop_patience_steps: int =-1,
start_padding_enabled = False,
val_check_steps: int = 100,
batch_size: int = 32,
valid_batch_size: Optional[int] = None,
windows_batch_size = 1024,
inference_windows_batch_size = 1024,
step_size: int = 1,
scaler_type: str = 'identity',
random_seed: int = 1,
num_workers_loader: int = 0,
drop_last_loader: bool = False,
optimizer=None,
optimizer_kwargs=None,
lr_scheduler = None,
lr_scheduler_kwargs = None,
**trainer_kwargs):
super(FEDformer, self).__init__(h=h,
input_size=input_size,
hist_exog_list=hist_exog_list,
stat_exog_list=stat_exog_list,
futr_exog_list = futr_exog_list,
loss=loss,
valid_loss=valid_loss,
max_steps=max_steps,
learning_rate=learning_rate,
num_lr_decays=num_lr_decays,
early_stop_patience_steps=early_stop_patience_steps,
val_check_steps=val_check_steps,
batch_size=batch_size,
windows_batch_size=windows_batch_size,
valid_batch_size=valid_batch_size,
inference_windows_batch_size=inference_windows_batch_size,
start_padding_enabled=start_padding_enabled,
step_size=step_size,
scaler_type=scaler_type,
num_workers_loader=num_workers_loader,
drop_last_loader=drop_last_loader,
random_seed=random_seed,
optimizer=optimizer,
optimizer_kwargs=optimizer_kwargs,
lr_scheduler=lr_scheduler,
lr_scheduler_kwargs=lr_scheduler_kwargs,
**trainer_kwargs)
# 建筑
self.label_len = int(np.ceil(input_size * decoder_input_size_multiplier))
if (self.label_len >= input_size) or (self.label_len <= 0):
raise Exception(f'Check decoder_input_size_multiplier={decoder_input_size_multiplier}, range (0,1)')
if activation not in ['relu', 'gelu']:
raise Exception(f'Check activation={activation}')
if n_head != 8:
raise Exception('n_head must be 8')
if version not in ['Fourier']:
raise Exception('Only Fourier version is supported currently.')
self.c_out = self.loss.outputsize_multiplier
self.output_attention = False
self.enc_in = 1
self.dec_in = 1
self.decomp = SeriesDecomp(MovingAvg_window)
# 嵌入
self.enc_embedding = DataEmbedding(c_in=self.enc_in,
exog_input_size=self.futr_exog_size,
hidden_size=hidden_size,
pos_embedding=False,
dropout=dropout)
self.dec_embedding = DataEmbedding(self.dec_in,
exog_input_size=self.futr_exog_size,
hidden_size=hidden_size,
pos_embedding=False,
dropout=dropout)
encoder_self_att = FourierBlock(in_channels=hidden_size,
out_channels=hidden_size,
seq_len=input_size,
modes=modes,
mode_select_method=mode_select)
decoder_self_att = FourierBlock(in_channels=hidden_size,
out_channels=hidden_size,
seq_len=input_size//2+self.h,
modes=modes,
mode_select_method=mode_select)
decoder_cross_att = FourierCrossAttention(in_channels=hidden_size,
out_channels=hidden_size,
seq_len_q=input_size//2+self.h,
seq_len_kv=input_size,
modes=modes,
mode_select_method=mode_select)
self.encoder = Encoder(
[
EncoderLayer(
AutoCorrelationLayer(
encoder_self_att,
hidden_size, n_head),
hidden_size=hidden_size,
conv_hidden_size=conv_hidden_size,
MovingAvg=MovingAvg_window,
dropout=dropout,
activation=activation
) for l in range(encoder_layers)
],
norm_layer=LayerNorm(hidden_size)
)
# 解码器
self.decoder = Decoder(
[
DecoderLayer(
AutoCorrelationLayer(
decoder_self_att,
hidden_size, n_head),
AutoCorrelationLayer(
decoder_cross_att,
hidden_size, n_head),
hidden_size=hidden_size,
c_out=self.c_out,
conv_hidden_size=conv_hidden_size,
MovingAvg=MovingAvg_window,
dropout=dropout,
activation=activation,
)
for l in range(decoder_layers)
],
norm_layer=LayerNorm(hidden_size),
projection=nn.Linear(hidden_size, self.c_out, bias=True)
)
def forward(self, windows_batch):
# 解析Windows批处理文件
insample_y = windows_batch['insample_y']
#insample_mask = windows_batch['insample_mask']
#hist_exog = windows_batch['hist_exog']
#stat_exog = windows_batch['stat_exog']
futr_exog = windows_batch['futr_exog']
# 解析输入
insample_y = insample_y.unsqueeze(-1) # [Ws,L,1]
if self.futr_exog_size > 0:
x_mark_enc = futr_exog[:,:self.input_size,:]
x_mark_dec = futr_exog[:,-(self.label_len+self.h):,:]
else:
x_mark_enc = None
x_mark_dec = None
x_dec = torch.zeros(size=(len(insample_y),self.h, self.dec_in), device=insample_y.device)
x_dec = torch.cat([insample_y[:,-self.label_len:,:], x_dec], dim=1)
# 分解初始化
mean = torch.mean(insample_y, dim=1).unsqueeze(1).repeat(1, self.h, 1)
zeros = torch.zeros([x_dec.shape[0], self.h, x_dec.shape[2]], device=insample_y.device)
seasonal_init, trend_init = self.decomp(insample_y)
# 解码器输入
trend_init = torch.cat([trend_init[:, -self.label_len:, :], mean], dim=1)
seasonal_init = torch.cat([seasonal_init[:, -self.label_len:, :], zeros], dim=1)
# 编码
enc_out = self.enc_embedding(insample_y, x_mark_enc)
enc_out, attns = self.encoder(enc_out, attn_mask=None)
# 十二月
dec_out = self.dec_embedding(seasonal_init, x_mark_dec)
seasonal_part, trend_part = self.decoder(dec_out, enc_out, x_mask=None, cross_mask=None,
trend=trend_init)
# 最终
dec_out = trend_part + seasonal_part
forecast = self.loss.domain_map(dec_out[:, -self.h:])
return forecastimport pandas as pd
import matplotlib.pyplot as plt
from neuralforecast import NeuralForecast
from neuralforecast.models import FEDformer
from neuralforecast.utils import AirPassengersPanel, augment_calendar_df
AirPassengersPanel, calendar_cols = augment_calendar_df(df=AirPassengersPanel, freq='M')
Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]] # 132次列车
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12项测试
model = FEDformer(h=12,
input_size=24,
modes=64,
hidden_size=64,
conv_hidden_size=128,
n_head=8,
loss=MAE(),
futr_exog_list=calendar_cols,
scaler_type='robust',
learning_rate=1e-3,
max_steps=500,
batch_size=2,
windows_batch_size=32,
val_check_steps=50,
early_stop_patience_steps=2)
nf = NeuralForecast(
models=[model],
freq='M',
)
nf.fit(df=Y_train_df, static_df=None, val_size=12)
forecasts = nf.predict(futr_df=Y_test_df)
Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])
plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)
plot_df = pd.concat([Y_train_df, plot_df])
if model.loss.is_distribution_output:
plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['FEDformer-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:],
y1=plot_df['FEDformer-lo-90'][-12:].values,
y2=plot_df['FEDformer-hi-90'][-12:].values,
alpha=0.4, label='level 90')
plt.grid()
plt.legend()
plt.plot()
else:
plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['FEDformer'], c='blue', label='Forecast')
plt.legend()
plt.grid()Give us a ⭐ on Github