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 9.54% per annum.
- UPS price at the close of November 19, 2024 was $133.20 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.15% per annum.
- UPS price at the close of November 19, 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 UPS 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: April 29, 2021
End date: November 19, 2024
a = 5.3963
b = -0.0003
s = 0.0645
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -9.54%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0645) – 1
= 29.45%
April 29, 2021 calculations
Top border of price channel:
Exp(Y361)
= Exp(a + b × X361 + 2 × s)
= Exp(a + b × 526 + 2 × s)
= Exp(5.3963 + -0.0003 × 526 + 2 × 0.0645)
= Exp(5.3809)
= $217.22
Bottom border of price channel:
Exp(Y361)
= Exp(a + b × X361 – 2 × s)
= Exp(a + b × 526 – 2 × s)
= Exp(5.3963 + -0.0003 × 526 – 2 × 0.0645)
= Exp(5.1228)
= $167.80
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.3963 + -0.0003 × 1,826 + 2 × 0.0645)
= Exp(5.0239)
= $152.00
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.3963 + -0.0003 × 1,826 – 2 × 0.0645)
= Exp(4.7657)
= $117.42
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 9.54% per annum.
- UPS price at the close of November 19, 2024 was $133.20 and was inside the primary price channel.
Secondary Trend
Start date: July 23, 2024
End date: November 19, 2024
a = 3.6576
b = 0.0007
s = 0.0155
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 28.15%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0155) – 1
= 6.39%
July 23, 2024 calculations
Top border of price channel:
Exp(Y1,173)
= Exp(a + b × X1,173 + 2 × s)
= Exp(a + b × 1,707 + 2 × s)
= Exp(3.6576 + 0.0007 × 1,707 + 2 × 0.0155)
= Exp(4.8484)
= $127.53
Bottom border of price channel:
Exp(Y1,173)
= Exp(a + b × X1,173 – 2 × s)
= Exp(a + b × 1,707 – 2 × s)
= Exp(3.6576 + 0.0007 × 1,707 – 2 × 0.0155)
= Exp(4.7865)
= $119.88
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.6576 + 0.0007 × 1,826 + 2 × 0.0155)
= Exp(4.9292)
= $138.27
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.6576 + 0.0007 × 1,826 – 2 × 0.0155)
= Exp(4.8673)
= $129.97
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.15% per annum.
- UPS price at the close of November 19, 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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