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 12.97% per annum.
- NKE price at the close of May 16, 2024 was $91.77 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 41.42% per annum.
- NKE price at the close of May 16, 2024 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 NKE 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: December 3, 2020
End date: May 16, 2024
a = 5.2576
b = -0.0004
s = 0.1175
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -12.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1175) – 1
= 60.02%
December 3, 2020 calculations
Top border of price channel:
Exp(Y391)
= Exp(a + b × X391 + 2 × s)
= Exp(a + b × 566 + 2 × s)
= Exp(5.2576 + -0.0004 × 566 + 2 × 0.1175)
= Exp(5.2773)
= $195.84
Bottom border of price channel:
Exp(Y391)
= Exp(a + b × X391 – 2 × s)
= Exp(a + b × 566 – 2 × s)
= Exp(5.2576 + -0.0004 × 566 – 2 × 0.1175)
= Exp(4.8072)
= $122.39
May 16, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.2576 + -0.0004 × 1,826 + 2 × 0.1175)
= Exp(4.7979)
= $121.25
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.2576 + -0.0004 × 1,826 – 2 × 0.1175)
= Exp(4.3278)
= $75.78
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 12.97% per annum.
- NKE price at the close of May 16, 2024 was $91.77 and was inside the primary price channel.
Secondary Trend
Start date: November 29, 2023
End date: May 16, 2024
a = 7.1711
b = -0.0015
s = 0.0383
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0015) – 1
= -41.42%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0383) – 1
= 16.55%
November 29, 2023 calculations
Top border of price channel:
Exp(Y1,142)
= Exp(a + b × X1,142 + 2 × s)
= Exp(a + b × 1,657 + 2 × s)
= Exp(7.1711 + -0.0015 × 1,657 + 2 × 0.0383)
= Exp(4.8200)
= $123.97
Bottom border of price channel:
Exp(Y1,142)
= Exp(a + b × X1,142 – 2 × s)
= Exp(a + b × 1,657 – 2 × s)
= Exp(7.1711 + -0.0015 × 1,657 – 2 × 0.0383)
= Exp(4.6669)
= $106.36
May 16, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(7.1711 + -0.0015 × 1,826 + 2 × 0.0383)
= Exp(4.5724)
= $96.78
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(7.1711 + -0.0015 × 1,826 – 2 × 0.0383)
= Exp(4.4192)
= $83.03
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 41.42% per annum.
- NKE price at the close of May 16, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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