Dummy Data

Using the definition of a fourier series, $$ \begin{aligned} S_i(t) &= \sum_{n=1}^N\left(a_n \cos\left(\frac{2\pi nt}{P_i}\right) + b_n \sin\left(\frac{2\pi nt}{P_i}\right)\right) \\ \end{aligned} $$ we create two series ($i\in\{1,2\}$) where $P_1 = 365$ and $P_2 = 30.5$ representing yearly and monthly seasonalities respectively for $N=3$.

P = 365
P2 = 30.5
N = 365
t = np.arange(N)

# Coefficients
an = [1, 0.5, -1.5]
bn = [1, -0.5, 1.5]

an2 = [-1, 0.5, -1.5]
bn2 = [1, -0.5, 2]

s = [a*np.cos(2*np.pi*(n+1)*t/P) + b*np.sin(2*np.pi*(n+1)*t/P)
     for n,(a,b) in enumerate(zip(an, bn))]
s2 = [a*np.cos(2*np.pi*(n+1)*t/P2) + b*np.sin(2*np.pi*(n+1)*t/P2)
     for n,(a,b) in enumerate(zip(an2, bn2))]

y = sum(s) + sum(s2)

plt.subplot(2,1,1)
plt.plot(t, sum(s), label='Yearly')
plt.plot(t, sum(s2), label='Monthly')
plt.legend()
plt.subplot(2,1,2)
plt.plot(t, y, label='Time Series')
plt.legend()
plt.show()

class FourierModel[source]

FourierModel(p:float=365.25, scale:float=1, n:int=7) :: Module

Block that outputs sin's and cos' as basis functions. parameters:

• p: period
• scale: time axis scaling factor
• n: number of fourier components

class Seasonal[source]

Seasonal(y_n=10, m_n=5, w_n=3, scale=1) :: Module

Combination of Fourier Blocks that gives weekly, monthly and yearly seasonality. parameters:

• y_n: Number of yearly components
• m_n: Number of monthly components
• w_n: Number of weekly components
• scale: time axis scaling factor

Testing

model = FourierModel()
learner = Learner(db, model, loss_func=F.l1_loss)
wd = 0
learner.lr_find(wd=wd)
learner.recorder.plot(skip_end=0)

LR Finder is complete, type {learner_name}.recorder.plot() to see the graph.

epochs = 5
learner.fit_one_cycle(epochs, 2e-1, wd=wd)

epoch	train_loss	valid_loss	time
0	2.521029	1.777201	00:00
1	2.403449	1.926800	00:00
2	2.249872	2.125787	00:00
3	2.135793	2.258477	00:00
4	2.054816	2.283656	00:00

y2 = learner.model(torch.Tensor(t)[:,None])
plt.plot(t, y, label='actual')
plt.plot(t, y2, label='prediction')
plt.show()

learner.model.plot()

model = Seasonal(w_n=0)
learner = Learner(db, model, loss_func=F.l1_loss)
wd = 0
learner.lr_find(wd=wd)
learner.recorder.plot(skip_end=0)

LR Finder is complete, type {learner_name}.recorder.plot() to see the graph.

epochs = 5
learner.fit_one_cycle(epochs, 2e-1, wd=wd)
y2 = learner.model(torch.Tensor(t)[:,None])
plt.plot(t, y, label='actual')
plt.plot(t, y2, label='prediction')
plt.show()

epoch	train_loss	valid_loss	time
0	2.303246	1.518271	00:00
1	2.102577	1.277658	00:00
2	1.778894	1.225464	00:00
3	1.478693	1.256059	00:00
4	1.256826	1.244654	00:00

learner.model.plot_components()