Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 0.94% per annum.
- LULU price at the close of May 6, 2024 was $350.24 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 32.05% per annum.
- LULU price at the close of May 6, 2024 was lower than the bottom border of the secondary price channel by $68.21 (16.30%). This indicates a possible reversal in the secondary trend direction.
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 LULU 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: May 29, 2020
End date: October 13, 2023
a = 5.8160
b = 0.0000
s = 0.1174
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 0.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1174) – 1
= 59.94%
May 29, 2020 calculations
Top border of price channel:
Exp(Y268)
= Exp(a + b × X268 + 2 × s)
= Exp(a + b × 388 + 2 × s)
= Exp(5.8160 + 0.0000 × 388 + 2 × 0.1174)
= Exp(6.0607)
= $428.70
Bottom border of price channel:
Exp(Y268)
= Exp(a + b × X268 – 2 × s)
= Exp(a + b × 388 – 2 × s)
= Exp(5.8160 + 0.0000 × 388 – 2 × 0.1174)
= Exp(5.5911)
= $268.03
October 13, 2023 calculations
Top border of price channel:
Exp(Y1,118)
= Exp(a + b × X1,118 + 2 × s)
= Exp(a + b × 1,620 + 2 × s)
= Exp(5.8160 + 0.0000 × 1,620 + 2 × 0.1174)
= Exp(6.0922)
= $442.40
Bottom border of price channel:
Exp(Y1,118)
= Exp(a + b × X1,118 – 2 × s)
= Exp(a + b × 1,620 – 2 × s)
= Exp(5.8160 + 0.0000 × 1,620 – 2 × 0.1174)
= Exp(5.6226)
= $276.60
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 0.94% per annum.
- LULU price at the close of May 6, 2024 was $350.24 and was inside the primary price channel.
Secondary Trend
Start date: May 9, 2022
End date: March 21, 2024
a = 4.7871
b = 0.0008
s = 0.0706
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 32.05%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0706) – 1
= 32.64%
May 9, 2022 calculations
Top border of price channel:
Exp(Y758)
= Exp(a + b × X758 + 2 × s)
= Exp(a + b × 1,098 + 2 × s)
= Exp(4.7871 + 0.0008 × 1,098 + 2 × 0.0706)
= Exp(5.7646)
= $318.81
Bottom border of price channel:
Exp(Y758)
= Exp(a + b × X758 – 2 × s)
= Exp(a + b × 1,098 – 2 × s)
= Exp(4.7871 + 0.0008 × 1,098 – 2 × 0.0706)
= Exp(5.4821)
= $240.35
March 21, 2024 calculations
Top border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 + 2 × s)
= Exp(a + b × 1,780 + 2 × s)
= Exp(4.7871 + 0.0008 × 1,780 + 2 × 0.0706)
= Exp(6.2840)
= $535.93
Bottom border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 – 2 × s)
= Exp(a + b × 1,780 – 2 × s)
= Exp(4.7871 + 0.0008 × 1,780 – 2 × 0.0706)
= Exp(6.0015)
= $404.04
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 32.05% per annum.
- LULU price at the close of May 6, 2024 was lower than the bottom border of the secondary price channel by $68.21 (16.30%). This indicates a possible reversal in the secondary trend direction.
- 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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