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 10.92% per annum.
- UPS price at the close of April 26, 2024 was $147.59 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 20.40% per annum.
- UPS price at the close of April 26, 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 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 28, 2021
End date: April 26, 2024
a = 5.6025
b = -0.0003
s = 0.0647
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.92%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0647) – 1
= 29.55%
April 28, 2021 calculations
Top border of price channel:
Exp(Y504)
= Exp(a + b × X504 + 2 × s)
= Exp(a + b × 730 + 2 × s)
= Exp(5.6025 + -0.0003 × 730 + 2 × 0.0647)
= Exp(5.5006)
= $244.84
Bottom border of price channel:
Exp(Y504)
= Exp(a + b × X504 – 2 × s)
= Exp(a + b × 730 – 2 × s)
= Exp(5.6025 + -0.0003 × 730 – 2 × 0.0647)
= Exp(5.2417)
= $188.99
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.6025 + -0.0003 × 1,824 + 2 × 0.0647)
= Exp(5.1539)
= $173.10
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.6025 + -0.0003 × 1,824 – 2 × 0.0647)
= Exp(4.8950)
= $133.62
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.92% per annum.
- UPS price at the close of April 26, 2024 was $147.59 and was inside the primary price channel.
Secondary Trend
Start date: January 31, 2023
End date: April 26, 2024
a = 6.1025
b = -0.0006
s = 0.0503
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -20.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0503) – 1
= 22.28%
January 31, 2023 calculations
Top border of price channel:
Exp(Y947)
= Exp(a + b × X947 + 2 × s)
= Exp(a + b × 1,373 + 2 × s)
= Exp(6.1025 + -0.0006 × 1,373 + 2 × 0.0503)
= Exp(5.3450)
= $209.56
Bottom border of price channel:
Exp(Y947)
= Exp(a + b × X947 – 2 × s)
= Exp(a + b × 1,373 – 2 × s)
= Exp(6.1025 + -0.0006 × 1,373 – 2 × 0.0503)
= Exp(5.1438)
= $171.37
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(6.1025 + -0.0006 × 1,824 + 2 × 0.0503)
= Exp(5.0631)
= $158.08
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.1025 + -0.0006 × 1,824 – 2 × 0.0503)
= Exp(4.8620)
= $129.28
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 20.40% per annum.
- UPS price at the close of April 26, 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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