Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 37.12% per annum.
- FIS price at the close of May 2, 2023 was $53.13 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 50.90% per annum.
- FIS price at the close of May 2, 2023 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of FIS price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: March 8, 2021
End date: May 2, 2023
a = 6.4120
b = -0.0013
s = 0.0852
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -37.12%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0852) – 1
= 40.62%
March 8, 2021 calculations
Top border of price channel:
Exp(Y715)
= Exp(a + b × X715 + 2 × s)
= Exp(a + b × 1,040 + 2 × s)
= Exp(6.4120 + -0.0013 × 1,040 + 2 × 0.0852)
= Exp(5.2606)
= $192.59
Bottom border of price channel:
Exp(Y715)
= Exp(a + b × X715 – 2 × s)
= Exp(a + b × 1,040 – 2 × s)
= Exp(6.4120 + -0.0013 × 1,040 – 2 × 0.0852)
= Exp(4.9197)
= $136.96
May 2, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(6.4120 + -0.0013 × 1,825 + 2 × 0.0852)
= Exp(4.2628)
= $71.01
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.4120 + -0.0013 × 1,825 – 2 × 0.0852)
= Exp(3.9220)
= $50.50
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 37.12% per annum.
- FIS price at the close of May 2, 2023 was $53.13 and was inside the primary price channel.
Secondary Trend
Start date: May 20, 2022
End date: May 2, 2023
a = 7.5451
b = -0.0019
s = 0.0867
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0019) – 1
= -50.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0867) – 1
= 41.46%
May 20, 2022 calculations
Top border of price channel:
Exp(Y1,020)
= Exp(a + b × X1,020 + 2 × s)
= Exp(a + b × 1,478 + 2 × s)
= Exp(7.5451 + -0.0019 × 1,478 + 2 × 0.0867)
= Exp(4.8382)
= $126.24
Bottom border of price channel:
Exp(Y1,020)
= Exp(a + b × X1,020 – 2 × s)
= Exp(a + b × 1,478 – 2 × s)
= Exp(7.5451 + -0.0019 × 1,478 – 2 × 0.0867)
= Exp(4.4913)
= $89.24
May 2, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(7.5451 + -0.0019 × 1,825 + 2 × 0.0867)
= Exp(4.1620)
= $64.20
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.5451 + -0.0019 × 1,825 – 2 × 0.0867)
= Exp(3.8151)
= $45.38
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 50.90% per annum.
- FIS price at the close of May 2, 2023 was inside the secondary price channel.
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