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 April 18, 2024 was $332.89 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.62% per annum.
- HD price at the close of April 18, 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 = 5.9192
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(Y487)
= Exp(a + b × X487 + 2 × s)
= Exp(a + b × 704 + 2 × s)
= Exp(5.9192 + -0.0001 × 704 + 2 × 0.0829)
= Exp(5.9896)
= $399.27
Bottom border of price channel:
Exp(Y487)
= Exp(a + b × X487 – 2 × s)
= Exp(a + b × 704 – 2 × s)
= Exp(5.9192 + -0.0001 × 704 – 2 × 0.0829)
= Exp(5.6579)
= $286.56
December 5, 2023 calculations
Top border of price channel:
Exp(Y1,165)
= Exp(a + b × X1,165 + 2 × s)
= Exp(a + b × 1,688 + 2 × s)
= Exp(5.9192 + -0.0001 × 1,688 + 2 × 0.0829)
= Exp(5.8563)
= $349.42
Bottom border of price channel:
Exp(Y1,165)
= Exp(a + b × X1,165 – 2 × s)
= Exp(a + b × 1,688 – 2 × s)
= Exp(5.9192 + -0.0001 × 1,688 – 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 April 18, 2024 was $332.89 and was inside the primary price channel.
Secondary Trend
Start date: May 5, 2022
End date: April 18, 2024
a = 5.3370
b = 0.0003
s = 0.0642
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 10.62%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0642) – 1
= 29.30%
May 5, 2022 calculations
Top border of price channel:
Exp(Y767)
= Exp(a + b × X767 + 2 × s)
= Exp(a + b × 1,109 + 2 × s)
= Exp(5.3370 + 0.0003 × 1,109 + 2 × 0.0642)
= Exp(5.7720)
= $321.17
Bottom border of price channel:
Exp(Y767)
= Exp(a + b × X767 – 2 × s)
= Exp(a + b × 1,109 – 2 × s)
= Exp(5.3370 + 0.0003 × 1,109 – 2 × 0.0642)
= Exp(5.5150)
= $248.40
April 18, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.3370 + 0.0003 × 1,823 + 2 × 0.0642)
= Exp(5.9693)
= $391.24
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.3370 + 0.0003 × 1,823 – 2 × 0.0642)
= Exp(5.7124)
= $302.59
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.62% per annum.
- HD price at the close of April 18, 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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