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 51.32% per annum.
- COST price at the close of May 12, 2025 was $1,016.15 and was lower than the bottom border of the primary price channel by $14.25 (1.38%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 23.80% per annum.
- COST price at the close of May 12, 2025 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 COST 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: December 15, 2022
End date: March 6, 2025
a = 4.9659
b = 0.0011
s = 0.0498
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 51.32%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0498) – 1
= 22.02%
December 15, 2022 calculations
Top border of price channel:
Exp(Y654)
= Exp(a + b × X654 + 2 × s)
= Exp(a + b × 946 + 2 × s)
= Exp(4.9659 + 0.0011 × 946 + 2 × 0.0498)
= Exp(6.1391)
= $463.63
Bottom border of price channel:
Exp(Y654)
= Exp(a + b × X654 – 2 × s)
= Exp(a + b × 946 – 2 × s)
= Exp(4.9659 + 0.0011 × 946 – 2 × 0.0498)
= Exp(5.9401)
= $379.97
March 6, 2025 calculations
Top border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 + 2 × s)
= Exp(a + b × 1,758 + 2 × s)
= Exp(4.9659 + 0.0011 × 1,758 + 2 × 0.0498)
= Exp(7.0607)
= $1,165.22
Bottom border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 – 2 × s)
= Exp(a + b × 1,758 – 2 × s)
= Exp(4.9659 + 0.0011 × 1,758 – 2 × 0.0498)
= Exp(6.8617)
= $954.95
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 51.32% per annum.
- COST price at the close of May 12, 2025 was $1,016.15 and was lower than the bottom border of the primary price channel by $14.25 (1.38%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: May 16, 2024
End date: May 12, 2025
a = 5.8546
b = 0.0006
s = 0.0411
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 23.80%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0411) – 1
= 17.86%
May 16, 2024 calculations
Top border of price channel:
Exp(Y1,009)
= Exp(a + b × X1,009 + 2 × s)
= Exp(a + b × 1,464 + 2 × s)
= Exp(5.8546 + 0.0006 × 1,464 + 2 × 0.0411)
= Exp(6.7931)
= $891.68
Bottom border of price channel:
Exp(Y1,009)
= Exp(a + b × X1,009 – 2 × s)
= Exp(a + b × 1,464 – 2 × s)
= Exp(5.8546 + 0.0006 × 1,464 – 2 × 0.0411)
= Exp(6.6288)
= $756.58
May 12, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.8546 + 0.0006 × 1,825 + 2 × 0.0411)
= Exp(7.0043)
= $1,101.32
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.8546 + 0.0006 × 1,825 – 2 × 0.0411)
= Exp(6.8400)
= $934.46
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 23.80% per annum.
- COST price at the close of May 12, 2025 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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