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 45.26% per annum.
- INTU price at the close of January 29, 2025 was $592.99 and was lower than the bottom border of the primary price channel by $180.39 (23.32%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.43% per annum.
- INTU price at the close of January 29, 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 INTU 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: September 21, 2022
End date: May 23, 2024
a = 4.8903
b = 0.0010
s = 0.0536
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 45.26%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0536) – 1
= 23.92%
September 21, 2022 calculations
Top border of price channel:
Exp(Y666)
= Exp(a + b × X666 + 2 × s)
= Exp(a + b × 965 + 2 × s)
= Exp(4.8903 + 0.0010 × 965 + 2 × 0.0536)
= Exp(5.9846)
= $397.24
Bottom border of price channel:
Exp(Y666)
= Exp(a + b × X666 – 2 × s)
= Exp(a + b × 965 – 2 × s)
= Exp(4.8903 + 0.0010 × 965 – 2 × 0.0536)
= Exp(5.7701)
= $320.58
May 23, 2024 calculations
Top border of price channel:
Exp(Y1,086)
= Exp(a + b × X1,086 + 2 × s)
= Exp(a + b × 1,575 + 2 × s)
= Exp(4.8903 + 0.0010 × 1,575 + 2 × 0.0536)
= Exp(6.6085)
= $741.35
Bottom border of price channel:
Exp(Y1,086)
= Exp(a + b × X1,086 – 2 × s)
= Exp(a + b × 1,575 – 2 × s)
= Exp(4.8903 + 0.0010 × 1,575 – 2 × 0.0536)
= Exp(6.3940)
= $598.27
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 45.26% per annum.
- INTU price at the close of January 29, 2025 was $592.99 and was lower than the bottom border of the primary price channel by $180.39 (23.32%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: December 12, 2023
End date: January 29, 2025
a = 6.3809
b = 0.0000
s = 0.0389
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.43%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0389) – 1
= 16.86%
December 12, 2023 calculations
Top border of price channel:
Exp(Y974)
= Exp(a + b × X974 + 2 × s)
= Exp(a + b × 1,412 + 2 × s)
= Exp(6.3809 + 0.0000 × 1,412 + 2 × 0.0389)
= Exp(6.5137)
= $674.34
Bottom border of price channel:
Exp(Y974)
= Exp(a + b × X974 – 2 × s)
= Exp(a + b × 1,412 – 2 × s)
= Exp(6.3809 + 0.0000 × 1,412 – 2 × 0.0389)
= Exp(6.3579)
= $577.06
January 29, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(6.3809 + 0.0000 × 1,826 + 2 × 0.0389)
= Exp(6.5298)
= $685.29
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.3809 + 0.0000 × 1,826 – 2 × 0.0389)
= Exp(6.3741)
= $586.43
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.43% per annum.
- INTU price at the close of January 29, 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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