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 4.83% per annum.
- HD price at the close of May 2, 2024 was $335.53 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.43% per annum.
- HD price at the close of May 2, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 HD 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 26, 2021
End date: December 5, 2023
a = 5.9177
b = -0.0001
s = 0.0829
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0829) – 1
= 39.33%
March 26, 2021 calculations
Top border of price channel:
Exp(Y478)
= Exp(a + b × X478 + 2 × s)
= Exp(a + b × 693 + 2 × s)
= Exp(5.9177 + -0.0001 × 693 + 2 × 0.0829)
= Exp(5.9896)
= $399.27
Bottom border of price channel:
Exp(Y478)
= Exp(a + b × X478 – 2 × s)
= Exp(a + b × 693 – 2 × s)
= Exp(5.9177 + -0.0001 × 693 – 2 × 0.0829)
= Exp(5.6579)
= $286.56
December 5, 2023 calculations
Top border of price channel:
Exp(Y1,156)
= Exp(a + b × X1,156 + 2 × s)
= Exp(a + b × 1,677 + 2 × s)
= Exp(5.9177 + -0.0001 × 1,677 + 2 × 0.0829)
= Exp(5.8563)
= $349.42
Bottom border of price channel:
Exp(Y1,156)
= Exp(a + b × X1,156 – 2 × s)
= Exp(a + b × 1,677 – 2 × s)
= Exp(5.9177 + -0.0001 × 1,677 – 2 × 0.0829)
= Exp(5.5246)
= $250.78
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 4.83% per annum.
- HD price at the close of May 2, 2024 was $335.53 and was inside the primary price channel.
Secondary Trend
Start date: May 5, 2022
End date: May 2, 2024
a = 5.3463
b = 0.0003
s = 0.0637
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 10.43%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0637) – 1
= 29.03%
May 5, 2022 calculations
Top border of price channel:
Exp(Y758)
= Exp(a + b × X758 + 2 × s)
= Exp(a + b × 1,098 + 2 × s)
= Exp(5.3463 + 0.0003 × 1,098 + 2 × 0.0637)
= Exp(5.7721)
= $321.20
Bottom border of price channel:
Exp(Y758)
= Exp(a + b × X758 – 2 × s)
= Exp(a + b × 1,098 – 2 × s)
= Exp(5.3463 + 0.0003 × 1,098 – 2 × 0.0637)
= Exp(5.5172)
= $248.94
May 2, 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(5.3463 + 0.0003 × 1,826 + 2 × 0.0637)
= Exp(5.9699)
= $391.45
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.3463 + 0.0003 × 1,826 – 2 × 0.0637)
= Exp(5.7150)
= $303.38
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.43% per annum.
- HD price at the close of May 2, 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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